A method of controlling the longitudinal density distribution of an ion beam in a storage ring

Abstract

This invention belongs to the field of ion beam control technology and discloses a method for controlling the longitudinal density distribution of an ion beam in a storage ring. The method includes: real-time detection of the actual length and longitudinal density distribution of an existing ion beam cluster within the storage ring; comparing the actual length of the ion beam cluster with a preset target length to determine whether the density distribution is too wide or too narrow; based on the determination result, generating a sawtooth wave modulation voltage through an electron gun of an electron cooling device; emitting an electron beam modulated by the sawtooth wave modulation voltage and matched to the velocity of the ion beam cluster; and differentially cooling the head, middle, and tail of the ion beam cluster through gentle collisions to adjust the longitudinal velocity distribution of the ions and adjust the sawtooth wave parameters to converge the cluster density to a narrow Gaussian distribution. This invention achieves precise control of the longitudinal density of the ion beam, with a simple structure and high efficiency.

Description

Technical Field

[0001] This invention relates to the field of ion beam modulation technology, and more specifically to a method for controlling the longitudinal density distribution of the ion beam in a storage ring. Background Technology

[0002] The longitudinal density distribution control of the ion beam involved in this invention is one of the techniques for optimizing the beam quality of heavy ion storage rings. It is widely used in particle physics experiments, nuclear physics research, ion beam applications and other fields. The uniformity and narrowing of the longitudinal density distribution of the ion beam directly determine the experimental accuracy and beam utilization efficiency.

[0003] In existing technologies, the ion beam within the storage ring is prone to longitudinal density distribution broadening and morphological distortion during cyclic flight due to factors such as microscopic thermal motion and the beam's own space charge effect, making it difficult to stably converge to a narrow Gaussian distribution. Traditional ion beam cooling and control methods mostly use a single-energy electron beam for overall cooling, which cannot achieve differentiated and precise control of the ion beam's head, middle, and tail, resulting in low cooling efficiency and poor control accuracy. While some improved schemes attempt to adjust the electron beam energy through voltage modulation, they lack a dynamic active control mechanism that matches the real-time ion beam morphology and do not feature functional zoning design for the storage ring's cooling and deflection sections, easily leading to mutual interference between cooling and deflection actions, further reducing the control effect. Moreover, existing technologies mostly passively adapt to the ion beam distribution morphology, failing to achieve directional guidance of ion density through active modulation of electron beam energy, thus limiting the flexibility and precision of control. Summary of the Invention

[0004] This invention provides a method for controlling the longitudinal density distribution of an ion beam in a storage ring, comprising: real-time detection of the actual length and longitudinal density distribution pattern of an existing ion beam cluster within the storage ring, comparing the actual length of the ion beam cluster with a preset target length, and determining whether the longitudinal density distribution pattern is too wide or too narrow; based on the determination result, generating a sawtooth wave modulation voltage through an electron gun of an electron cooling device, and emitting an electron beam modulated by the sawtooth wave modulation voltage and matching the velocity of the ion beam cluster, utilizing the small relative velocities generated by the microscopic thermal motion between ions and electrons to conduct gentle collisions, thereby implementing differentiated cooling of the head, middle, and tail of the ion beam cluster to adjust the longitudinal velocity distribution of the ions; wherein the electron beam is modulated by the sawtooth wave modulation voltage to form a longitudinal energy gradient; and continuously adjusting the parameters of the sawtooth wave modulation voltage according to the real-time pattern of the ion beam cluster, so that the longitudinal density distribution of the ion beam cluster converges to a narrowed Gaussian distribution.

[0005] According to one embodiment of the present invention, the real-time detection of the actual length and longitudinal density distribution of the existing ion beam clusters within the storage ring, the emission of an electron beam modulated by the sawtooth wave modulation voltage and matched to the velocity of the ion beam clusters, and the occurrence of a mild collision are all performed in the cooling section of the electron cooling device of the storage ring.

[0006] According to one embodiment of the present invention, the direction of the sawtooth wave modulation voltage is matched with the longitudinal density distribution pattern of the ion beam: if the longitudinal density distribution pattern of the ion beam is found to be too narrow, a sawtooth wave modulation voltage with a positive slope is used to make the electron beam form a longitudinal energy gradient with a low head and high tail, so as to stretch the ion beam; if the longitudinal density distribution pattern of the ion beam is found to be too wide, a sawtooth wave modulation voltage with a negative slope is used to make the electron beam form a longitudinal energy gradient with a high head and low tail, so as to compress the ion beam.

[0007] According to one embodiment of the present invention, the differential cooling of the head, middle and tail of the ion beam cluster to adjust the longitudinal velocity distribution of the ions specifically includes: applying continuously varying cooling forces of different intensities to the fast ions at the head, the middle ions and the slow ions at the tail along the entire length of the ion beam cluster through the longitudinal energy gradient of the electron beam, adjusting the longitudinal velocity difference between the ions, thereby controlling the ion beam cluster to achieve aggregation or dispersion.

[0008] According to one embodiment of the present invention, a strong cooling force is applied to the head fast ions of the ion beam cluster to reduce the longitudinal velocity of the head fast ions; the sawtooth wave modulation voltage corresponding to the strong cooling force has a large absolute slope, and the sawtooth wave modulation voltage has a short scan rise time for the ion beam cluster per unit time.

[0009] According to one embodiment of the present invention, a moderate cooling force is applied to the intermediate ions of the ion beam to maintain the longitudinal velocity of the intermediate ions; the sawtooth wave modulation voltage corresponding to the moderate cooling force has a moderate absolute slope, and the sawtooth wave modulation voltage has a moderate scan rise time for the ion beam per unit time.

[0010] According to one embodiment of the present invention, a weak cooling force is applied to the slow ions at the tail of the ion beam cluster to maintain or increase the longitudinal velocity of the slow ions at the tail; the sawtooth wave modulation voltage corresponding to the weak cooling force has a small absolute slope, and the sawtooth wave modulation voltage has a long scan rise time for the ion beam cluster per unit time.

[0011] According to one embodiment of the present invention, when the sawtooth wave modulation voltage has a positive slope, the ion beam is stretched; when the sawtooth wave modulation voltage has a negative slope, the ion beam is compressed.

[0012] This invention addresses the shortcomings of passive adaptation in existing technologies by enabling bidirectional adjustment of ion beam length, balancing ion beam stability and brightness. By matching the positive and negative polarity slopes of the sawtooth wave modulation voltage to the actual shape of the ion beam, it longitudinally stretches excessively short ion beams, alleviating intra-beam scattering problems caused by dense ion distribution at the center of the ion beam, reducing inter-ion repulsion, improving the overall stability of the ion beam, and extending ion lifetime. Simultaneously, it longitudinally compresses excessively long ion beams, improving the non-concentrated ion distribution and effectively enhancing the brightness of the ion beam, thus achieving an optimal trade-off between ion beam length and density distribution.

[0013] This invention offers superior control precision, enabling the longitudinal distribution of the ion beam to conform to the Gaussian distribution. The sawtooth wave modulation voltage achieves spatial gradient modulation of the instantaneous energy of the electron beam, allowing the electron beam to form a uniform and monotonically changing longitudinal energy gradient and cooling rate gradient along the entire length of the ion beam cluster. The absolute value of the slope of the sawtooth wave modulation voltage can be flexibly adapted according to the envelope distribution of the ion beam cluster, precisely controlling the longitudinal drift direction and drift velocity of the ions. This gradually drives the longitudinal density distribution of the ion beam to converge to a narrow Gaussian distribution, meeting the requirements of physical experiments for small ion beam velocity differences and concentrated distribution, and adapting to higher precision scientific research scenarios.

[0014] This invention realizes the transformation of electron beam control of ion beam from passive adaptation to active manipulation. By actively modulating the energy dispersion of the electron beam through composite voltage waveform, the energy distribution of the electron beam is precisely matched with the longitudinal phase space of the ion beam. This changes the time structure of cooling efficiency, and instead of passively adapting to the spatial distribution of the ion beam, it actively guides the redistribution of ion density, fundamentally optimizing the longitudinal density distribution of the ion beam. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0016] Figure 1 This is a schematic flowchart of the method for controlling the longitudinal density distribution of the ion beam in the storage ring provided by the present invention.

[0017] Figure 2 This is a graph showing the relationship between the amplitude of the negative slope sawtooth wave sweep period and the sweep time t provided by the present invention.

[0018] Figure 3 This is a graph showing the relationship between the amplitude of the positive slope sawtooth wave sweep period and the sweep time t provided by the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0020] The following is combined with Figures 1 to 3 The present invention describes a method for controlling the longitudinal density distribution of the ion beam in a storage ring. Figure 1 This is a schematic flowchart of the method for controlling the longitudinal density distribution of the ion beam in a storage ring provided by the present invention. Figure 1 As shown, the method for controlling the longitudinal density distribution of an ion beam in a storage ring provided by the present invention includes: in step S100, the actual length and longitudinal density distribution pattern of an existing ion beam cluster in the storage ring are detected in real time, and the actual length of the ion beam cluster is compared with a preset target length to determine whether the longitudinal density distribution pattern is too wide or too narrow; in step S200, according to the determination result, a sawtooth wave modulation voltage is generated by the electron gun of the electron cooling device, and an electron beam modulated by the sawtooth wave modulation voltage and matched with the velocity of the ion beam cluster is emitted. The small relative velocity generated by the microscopic thermal motion between ions and electrons causes a gentle collision, and differential cooling is performed on the head, middle and tail of the ion beam cluster to adjust the longitudinal velocity distribution of ions; wherein, the electron beam is modulated by the sawtooth wave modulation voltage to form a longitudinal energy gradient; in step S300, according to the real-time shape of the ion beam cluster, the parameters of the sawtooth wave modulation voltage are continuously adjusted so that the longitudinal density distribution of the ion beam cluster converges to a narrow Gaussian distribution.

[0021] Specifically, the method for controlling the longitudinal density distribution of the ion beam in the storage ring provided by the present invention, in step S100, involves the ion bundle monitoring unit monitoring the actual length of the ion bundle. Real-time detection of longitudinal density distribution morphology is performed without interfering with the normal operation of the ion beam cluster. The actual length of the ion beam cluster is compared with the preset target length. By comparison, it was determined whether the density distribution pattern was too wide or too narrow. The entire detection operation was completed in the cooling section of the storage ring, which effectively avoided magnetic field interference and ensured the accuracy of the detection data.

[0022] In step S200, the electron gun of the electron cooling device generates a sawtooth wave modulation voltage based on the judgment result. This voltage modulates the energy distribution of the electron beam, causing the electron beam to form a longitudinal energy gradient adapted to the ion cluster. The voltage output of the electron gun is dynamically matched with the velocity of the ion cluster to ensure the effectiveness of gentle collisions. The electron beam cooling unit achieves instantaneous modulation of electron energy by superimposing a sawtooth wave modulation voltage on the DC bias high voltage of the cathode of the electron cooling electron gun to form a composite voltage waveform. The function of the composite voltage waveform is: ; in, It is a cathode DC bias high voltage. The amplitude control function for sawtooth wave modulation voltage is expressed as follows: ; In the formula, The initial amplitude of the sawtooth wave modulated voltage. For frequency sweep time, It is the exponential decay constant. The normalized sawtooth function is defined as follows: ; in, To accumulate phase, ensure a constant slope within each sawtooth and continuous overall frequency sweep; the instantaneous frequency of the sawtooth wave. With sweep frequency period satisfy: ; in, This is the start frequency for the frequency sweep. For the scanning rate, this function ensures that the instantaneous frequency of the sawtooth wave continuously decreases with the sweep time, while the sweep period gradually increases with the sweep time. This results in the modulated electron beam producing a monotonically varying average energy at different longitudinal positions. The modulation frequency of the electron beam is consistent with, or is a harmonic, second harmonic, or multiple harmonic of the ion beam's cyclotron frequency, ensuring precise overlap between the electron and ion beams during their cyclic flight through the storage ring, guaranteeing a stable and efficient cooling process. Ions and electrons generate minute relative velocities due to microscopic thermal motion, resulting in gentle collisions. The electron beam cooling unit utilizes this collision process to apply differentiated cooling to the head, middle, and tail of the ion beam, thereby adjusting the longitudinal velocity distribution of the ions. Both the emission of the electron beam and the gentle collisions between ions and electrons are completed within the cooling section of the storage ring. The electron beam cooling unit applies continuously varying cooling forces of different intensities to the fast ions at the head, middle ions, and slow ions at the tail along the entire length of the ion beam using the longitudinal energy gradient of the electron beam, adjusting the longitudinal velocity difference between the ions and thus controlling the convergence or dispersion of the ion beam. A strong cooling force is applied to the fast ions at the head to reduce their longitudinal velocity. The sawtooth wave modulation voltage corresponding to this strong cooling force has a large absolute slope, resulting in a short scan rise time for the ion bundle per unit time. A moderate cooling force is applied to the middle ions to maintain their longitudinal velocity. The sawtooth wave modulation voltage corresponding to this moderate cooling force has a medium absolute slope, resulting in a medium scan rise time for the ion bundle per unit time. A weak cooling force is applied to the slow ions at the tail to maintain or increase their longitudinal velocity. The sawtooth wave modulation voltage corresponding to this weak cooling force has a small absolute slope, resulting in a long scan rise time for the ion bundle per unit time. The direction of the sawtooth wave modulation voltage is matched to the longitudinal density distribution of the ion bundle. The actual length of the ion bundle detected by the bundle monitoring unit is... Less than the preset target length When the longitudinal density distribution of the ion beam is too narrow, the electron beam cooling unit uses a sawtooth wave modulation voltage with a positive slope to create a longitudinal energy gradient with a low head and high tail, thus stretching the ion beam longitudinally. The actual length of the ion beam detected by the beam monitoring unit... Greater than the preset target length When the longitudinal density distribution of the ion beam is too wide, the electron beam cooling unit uses a sawtooth wave modulation voltage with a negative slope to create a longitudinal energy gradient with a high head and low tail, thereby compressing the ion beam in the longitudinal direction.

[0023] In step S300, the parameter control unit receives real-time morphology data of the ion bundle from the bundle monitoring unit, and continuously adjusts the parameters of the sawtooth wave modulation voltage based on this data. The slope function of the sawtooth wave modulation voltage is: ; In the formula, The initial amplitude of the sawtooth wave modulated voltage. Instantaneous frequency, The exponential decay factor is used. The parameter control unit, as the main unit of overall control, changes the slope characteristics of the sawtooth wave modulation voltage by adjusting relevant parameters, thereby transmitting control signals to the electron beam cooling unit. This adjusts the longitudinal energy gradient and cooling force distribution of the electron beam output by the electron beam cooling unit. The larger the absolute value of the sawtooth wave modulation voltage slope per unit time, the shorter the rise time of the scanning ion cluster, the stronger the cooling force of the electron beam cooling unit on the ion cluster, the faster the ion drift velocity, and the faster the change in ion density distribution. The parameter control unit thus precisely controls the longitudinal drift direction and velocity of the ions, causing the longitudinal density distribution of the ion cluster to gradually converge to a narrow Gaussian distribution. The exponential decay factor effectively prevents long-term DC component drift, ensures a consistent gradient direction of the cooling rate, and avoids overshoot problems in beam length adjustment. The parameter control unit, through dynamic adjustment of the sawtooth wave modulation voltage parameters, works in conjunction with the ion acceleration unit, ion implantation unit, magnetic field application unit, cluster monitoring unit, and electron beam cooling unit. Utilizing the functional partition design of the storage ring, detection, cooling, and deflection actions do not interfere with each other, improving overall control efficiency and accuracy. Among them, the cluster monitoring unit, electron beam cooling unit, and parameter control unit are all located in the cooling section of the electron cooling device of the storage ring; the ion acceleration unit is located in the high-frequency cavity of the straight section of the storage ring, and the ion implantation unit is located in the diode position of the curved section. The diode constitutes the magnetic field application unit of the present invention. Each unit is set in a partition, works independently, and does not interfere with each other.

[0024] According to an embodiment of the present invention, the real-time detection of the actual length and longitudinal density distribution of the existing ion clusters within the storage ring, the emission of an electron beam modulated by a sawtooth wave modulation voltage and matched to the velocity of the ion clusters, and the occurrence of mild collisions are all performed in the cooling section of the electron cooling device of the storage ring.

[0025] Specifically, this invention ensures precise implementation of the control method by clearly defining the dedicated functions of each area: the cooling section of the storage ring serves as the main area for ion beam control, where all key operations related to differentiated cooling are performed, and the magnetic field-free environment of the cooling section is precisely matched to the electron gun output of the electron cooling device. The beam monitoring unit monitors the actual length of the ion beam. The real-time detection of the longitudinal density distribution pattern is completed entirely in the cooling section of the storage ring. This region is free from the interference of the deflection magnetic field, which can effectively ensure the stability of the detection signal and the accuracy of the detection data. It can capture the length changes and density distribution pattern characteristics of the ion beam in real time and accurately, providing a reliable basis for subsequent differentiated cooling control.

[0026] The action of the electron beam cooling unit emitting an electron beam with a velocity matching that of the ion beam cluster is also carried out in the cooling section of the storage ring. After receiving the control command from the electron beam cooling unit, the electron beam modulated by the sawtooth wave modulation voltage can be accurately emitted in the cooling section, so that the electron beam can accurately meet the ion beam cluster in this region, preparing for the subsequent gentle collision.

[0027] The gentle collisions between ions and electrons, caused by the tiny relative velocities generated by microscopic thermal motion, also occur in the cooling section of the storage ring. The modulated electron beam and ion clusters come into full contact and collide within the cooling section. The electron beam cooling unit uses this collision process to perform differentiated cooling on the head, middle, and tail of the ion clusters, adjusting the longitudinal velocity distribution of the ions. The magnetic field-free environment of the cooling section makes the collision process between the electron beam and the ion clusters more stable, allowing for more precise control of the differentiated cooling effect and avoiding interference from the magnetic field on the collision process and cooling effect.

[0028] Based on this functional zoning design, the detection of ion beam clusters, electron beam emission, and gentle collision cooling are carried out in an orderly manner in the cooling section, making the entire longitudinal density distribution control process of the ion beam more efficient and precise, and effectively solving the problem of poor control effect caused by the mixing of functional regions in traditional technologies.

[0029] According to an embodiment of the present invention, the direction of the sawtooth wave modulation voltage is matched with the longitudinal density distribution pattern of the ion beam: if the longitudinal density distribution pattern of the ion beam is found to be too narrow, a sawtooth wave modulation voltage with a positive slope is used to make the electron beam form a longitudinal energy gradient with a low head and high tail, so as to stretch the ion beam; if the longitudinal density distribution pattern of the ion beam is found to be too wide, a sawtooth wave modulation voltage with a negative slope is used to make the electron beam form a longitudinal energy gradient with a high head and low tail, so as to compress the ion beam.

[0030] Specifically, the slope selection of the sawtooth wave modulation voltage and its adaptation to the ion beam cluster morphology are precisely achieved through the electron gun of the electron cooling device: the electron gun outputs a modulation voltage with a positive or negative slope based on the density distribution information fed back by the cluster monitoring unit, ensuring a precise match between the energy gradient of the electron beam and the cluster control requirements. In this invention, the modulation direction of the sawtooth wave modulation voltage forms a precise adaptation and control relationship with the longitudinal density distribution morphology of the ion beam cluster, and the electron beam cooling unit adjusts the modulation voltage based on the actual length of the ion beam cluster fed back by the cluster monitoring unit. With the preset target length Based on the comparison results and the envelope distribution of the ion beam, a sawtooth wave modulation voltage with a positive or negative slope is output. By modulating the longitudinal energy gradient characteristics of the electron beam, the longitudinal stretching or compression of the ion beam is achieved, thereby optimizing the longitudinal density distribution of the ion beam and taking into account both the stability and brightness of the beam.

[0031] When the cluster monitoring unit detects and determines the actual length of the ion cluster Less than the preset target length When the ion beam exhibits an excessively narrow longitudinal density distribution, the electron beam cooling unit will output a sawtooth wave modulation voltage with a positive slope, such as... Figure 3 Slope sawtooth wave sweep period amplitude and sweep time As shown in the relationship, the amplitude of the positive-slope sawtooth wave modulation voltage continuously increases with the sweep time, the instantaneous frequency continuously decreases with the sweep time, the sweep period gradually increases with time, and the retrace time is approximately 0, enabling full-length longitudinal gradient coverage sweep of the ion beam. After the positive-slope sawtooth wave modulation voltage modulates the electron beam, it creates a longitudinal energy gradient with a lower head and a higher tail. The electron beam exhibits a lower average energy in the head region and a higher average energy in the tail region, forming a monotonically increasing energy distribution from head to tail. Based on this energy gradient, when ions and electrons undergo gentle collisions, the cooling force at different positions of the ion beam forms a corresponding gradient distribution, pushing the ions to drift away from the center frequency, achieving longitudinal stretching of the ion beam. This effectively alleviates the problem of dense central ion distribution caused by an excessively narrow ion beam, reduces mutual repulsion between ions, decreases intra-beam scattering, extends ion lifetime, and improves the overall stability of the ion beam.

[0032] When the cluster monitoring unit detects and determines the actual length of the ion cluster Greater than the preset target length When the ion beam exhibits an excessively wide longitudinal density distribution, the electron beam cooling unit will output a sawtooth wave modulation voltage with a negative slope, such as... Figure 2 Slope sawtooth wave sweep period amplitude and sweep time As shown in the figure, the amplitude of the negative-slope sawtooth wave modulation voltage continuously decreases with the sweep time, the instantaneous frequency continuously decreases with the sweep time, the sweep period gradually increases with time, and the retrace time is also approximately 0, enabling uniform gradient sweeping of the entire length of the ion beam. In the figure, T represents the sweep period. After the negative-slope sawtooth wave modulation voltage modulates the electron beam, it creates a longitudinal energy gradient with a high head and low tail. The electron beam exhibits a higher average energy in the head region of the ion beam and a lower average energy in the tail region, forming a monotonically decreasing energy distribution from head to tail. Under this energy gradient, during the gentle collision between ions and electrons, the head and tail of the ion beam will be subjected to a directional cooling force, pulling the ions to drift towards the center frequency, achieving longitudinal compression of the ion beam. This improves the problem of non-concentrated ion distribution caused by an excessively wide ion beam, making the longitudinal density distribution of the ion beam more compact, effectively improving the brightness of the ion beam, and meeting the requirements of concentrated ion beam distribution in physical experiments.

[0033] The modulation of both positive and negative slope sawtooth wave modulation voltages is achieved by superimposing sawtooth wave modulation voltages of corresponding slopes onto the DC bias high voltage of the electron-cooled electron gun cathode. Both follow the laws of sawtooth wave amplitude control and slope function; the amplitude changes continuously with the sweep time, the instantaneous frequency changes continuously with the sweep time, and the absolute value of the slope can be flexibly adapted according to the envelope distribution of the ion beam. Figure 2 , Figure 3 The sawtooth wave modulation characteristics, with both slopes, ensure that the longitudinal energy gradient of the electron beam completely covers the entire length of the ion bundle, forming a uniformly oriented and monotonically varying cooling rate gradient at the head, middle, and tail of the ion bundle. Regardless of whether a positive or negative slope sawtooth wave is used to modulate the voltage, precise adjustment of the longitudinal density distribution of the ion bundle can be achieved through energy gradient control without altering the average cooling energy of the electron beam, allowing the length of the ion bundle to gradually move towards the preset target length. The convergence process eventually stabilizes the longitudinal density distribution of the ion beam cluster to a narrow Gaussian distribution, achieving an optimal trade-off between the length and density distribution of the ion beam cluster.

[0034] According to an embodiment of the present invention, differential cooling is applied to the head, middle and tail of the ion beam cluster to adjust the longitudinal velocity distribution of the ions. Specifically, this includes applying continuously varying cooling forces of different intensities to the fast ions at the head, the middle ions and the slow ions at the tail along the entire length of the ion beam cluster using the longitudinal energy gradient of the electron beam, thereby adjusting the longitudinal velocity difference between the ions and controlling the ion beam cluster to achieve aggregation or dispersion.

[0035] Specifically, differentiated cooling relies on the sawtooth-wave modulated voltage output by the electron gun of the electron cooling device. The longitudinal energy gradient of the electron beam formed by this voltage modulation provides support for the continuous variation and precise adaptation of the cooling force. The cooling force generated during the gentle collision between ions and electrons is the directional deceleration force exerted by the electrons on the ions after the collision of small relative velocities based on microscopic thermal motion. The magnitude of this force is directly related to the energy gradient of the electron beam and can be adapted and controlled according to the flight speed of the ions. It is the main force for achieving differentiated cooling of the ion beam. The electron beam modulated by the sawtooth-wave modulated voltage has a continuously varying longitudinal energy gradient. This energy gradient is distributed along the entire length of the ion beam and precisely matches the longitudinal position of the ion beam. Relying on this energy gradient characteristic, the electron beam cooling unit forms a differentiated cooling effect on the fast ions at the head, the middle ions, and the slow ions at the tail of the ion beam. By applying continuously varying cooling forces of different intensities, the longitudinal velocity difference of the ions is precisely adjusted, thereby controlling the ion beam to complete the control action of focusing or dispersing.

[0036] As the ion beam circulates within the storage ring, the fastest-moving ions arrive first at the designated cross-section, forming the ion beam head. Slower-moving ions arrive later, forming the ion beam tail, while intermediate ions maintain a moderate velocity. These three ions together form an ion beam with a longitudinal velocity difference. The electron beam output from the electron beam cooling unit is modulated so that its longitudinal energy gradient matches the longitudinal velocity distribution of the ion beam. This creates a sequentially varying cooling force intensity at the head, middle, and tail of the ion beam. The continuous variation of this cooling force matches the longitudinal density distribution of the ion beam, uninterruptedly covering its entire length and ensuring that ions at each longitudinal position receive an appropriate cooling force.

[0037] For the fast ions at the head of the ion beam cluster, the longitudinal energy gradient of the electron beam creates a strong cooling force in this region. This strong cooling force can rapidly reduce the longitudinal velocity of the fast ions, causing their velocity to approach the average velocity of the ion beam cluster. For the middle ions of the ion beam cluster, the longitudinal energy gradient of the electron beam creates a moderate cooling force in this region. This moderate cooling force can maintain the longitudinal velocity of the middle ions, maintain the stability of the middle region of the ion beam cluster, and avoid density distribution disorder caused by sudden velocity changes. For the slow ions at the tail of the ion beam cluster, the longitudinal energy gradient of the electron beam creates a weak cooling force in this region. This weak cooling force can maintain or even appropriately increase the longitudinal velocity of the slow ions, causing their velocity to also approach the average velocity of the ion beam cluster.

[0038] By applying continuously varying cooling forces of different intensities to the fast ions at the head, the middle ions, and the slow ions at the tail, the longitudinal velocity difference between ions at different locations within the ion cluster is gradually adjusted, achieving orderly alignment of ion flight velocities. When the longitudinal density distribution of the ion cluster is too wide, this differentiated cooling effect pulls ions with different velocities towards the central region of the ion cluster, reducing the longitudinal distribution range and achieving cluster convergence. When the longitudinal density distribution of the ion cluster is too narrow, this differentiated cooling effect promotes the ions to disperse appropriately to both sides of the ion cluster, expanding the longitudinal distribution range and achieving cluster dispersion. Throughout the entire cooling adjustment process, the cooling force remains continuously varied along the entire length of the ion cluster without abrupt changes, ensuring a smooth adjustment of the longitudinal velocity distribution of the ion cluster and avoiding distortion of the ion cluster shape due to sudden changes in cooling force, thus guaranteeing the smoothness and precision of the longitudinal density distribution control.

[0039] According to an embodiment of the present invention, a strong cooling force is applied to the fast ions at the head of the ion beam to reduce the longitudinal velocity of the fast ions at the head; the sawtooth wave modulation voltage corresponding to the strong cooling force has a large absolute slope, and the sawtooth wave modulation voltage has a short scan rise time for the ion beam per unit time.

[0040] Specifically, the strong cooling force control of fast ions at the head is precisely achieved through the sawtooth wave modulation voltage output by the electron gun of the electronic cooling device: based on the fast ion velocity information fed back by the cluster monitoring unit, the electron gun outputs a modulation voltage with a large absolute slope, providing energy support for the strong cooling force. The fast ions at the head of the ion cluster are the ions that arrive at the designated cross-section first during their circulating flight within the storage ring. Their longitudinal flight velocity is significantly higher than the average velocity of the ion cluster, which is the key factor causing the longitudinal velocity difference of the ion cluster and affecting the uniformity of the density distribution. It is necessary to achieve rapid and directional deceleration control through strong cooling force, so that the longitudinal velocity of the fast ions approaches the average velocity of the ion cluster, laying the foundation for optimizing the overall density distribution of the ion cluster.

[0041] The generation of this strong cooling force is directly related to the characteristics of the sawtooth wave modulation voltage. The sawtooth wave modulation voltage has a large absolute slope, which determines that the amplitude of the sawtooth wave modulation voltage changes rapidly during the frequency sweep process. This causes the electron beam modulated by the voltage to form a distribution pattern with a rapid energy gradient. The electron beam forms a high-energy distribution in the head region of the ion cluster. When it collides gently with the fast ions, it generates a stronger directional deceleration force, i.e., a strong cooling force. This strong cooling force can act precisely on the fast ions at the head, efficiently counteracting the excess kinetic energy of the fast ions and rapidly reducing their longitudinal velocity, without causing excessive cooling interference to ions in other positions of the ion cluster.

[0042] Complementing the sawtooth wave modulation voltage with its large absolute slope is its short scan rise time for the ion beam. This short rise time means the sawtooth wave modulation voltage can complete a frequency sweep across the ion beam head region in an extremely short time, allowing the strong cooling force to act rapidly and continuously on the fast ions at the head. This avoids the problem of fast ions continuing to fly forward during cooling due to excessively long scan rise times, which could cause positional shifts and disordered density distribution at the ion beam head. Simultaneously, the short rise time allows the energy of the sawtooth wave modulation voltage to be rapidly concentrated in the ion beam head region, ensuring precise matching between the electron beam energy gradient and the position of the fast ions at the head. This optimizes the efficiency of the strong cooling force, enabling efficient and precise control of the longitudinal velocity of the fast ions at the head.

[0043] Based on the velocity and distribution information of fast ions at the head of the ion cluster fed back by the cluster monitoring unit, the electron beam cooling unit outputs a sawtooth wave modulation voltage with a large absolute slope and a short scan rise time through parameter control by the parameter control unit. After the electron beam is modulated by this voltage, an energy gradient adapted to the fast ions at the head is formed in the cooling section of the storage ring, resulting in a gentle collision with the fast ions and generating a strong cooling force. The strong cooling force acts directionally on the longitudinal flight direction of the fast ions at the head, gradually reducing their flight velocity until the longitudinal velocity of the fast ions approaches the average velocity of the ion cluster. This effectively reduces the longitudinal velocity difference within the ion cluster, providing a stable velocity basis for subsequent ion cluster focusing or stretching control. At the same time, this control process is completed entirely in the cooling section of the storage ring, without interference from the deflection magnetic field, ensuring that the deceleration control of the fast ions at the head by the strong cooling force is always precise and stable.

[0044] According to an embodiment of the present invention, a moderate cooling force is applied to the intermediate ions of the ion beam to maintain the longitudinal velocity of the intermediate ions; the sawtooth wave modulation voltage corresponding to the moderate cooling force has a moderate absolute slope, and the sawtooth wave modulation voltage has a moderate scan rise time for the ion beam per unit time.

[0045] Specifically, the moderate cooling force control of intermediate ions is precisely achieved through the sawtooth wave modulation voltage output by the electron gun of the electronic cooling device: based on the intermediate ion velocity stability information fed back by the cluster monitoring unit, the electron gun outputs a modulation voltage with a moderate absolute slope, providing appropriate energy support for the moderate cooling force. The intermediate ions in the ion cluster are the main group with longitudinal velocities close to the average cluster velocity. Their velocity stability directly determines the regularity of the overall ion cluster morphology and serves as the velocity transition region connecting the fast ions at the head and the slow ions at the tail. Applying a moderate cooling force to the intermediate ions aims to maintain their original longitudinal velocity, avoiding velocity decreases due to excessive cooling force or velocity deviation due to insufficient cooling force, thereby ensuring the continuity and smoothness of the longitudinal velocity distribution of the ion cluster and providing stable intermediate support for the differentiated control of head and tail ions.

[0046] The generation of moderate cooling force is determined by the corresponding sawtooth wave modulation voltage characteristics. This sawtooth wave modulation voltage has a moderate absolute slope, and its amplitude change rate lies between the large absolute slope corresponding to strong cooling force and the small absolute slope corresponding to weak cooling force. This gentle slope characteristic allows the modulated electron beam to form a uniform and moderate energy distribution in the intermediate ion region. When it collides gently with the intermediate ions, the resulting directional deceleration force neither excessively cancels out the kinetic energy of the intermediate ions nor effectively cancels out the velocity fluctuations caused by microscopic thermal motion, thus achieving precise maintenance of the longitudinal velocity of the intermediate ions. At the same time, the sawtooth wave modulation voltage with a moderate absolute slope allows the electron beam energy gradient to maintain a smooth transition in the middle region, avoiding abrupt changes in the cooling force at the head and tail, and ensuring a continuous and coordinated cooling force distribution along the entire length of the ion beam cluster.

[0047] Matching the moderate absolute slope, the sawtooth wave modulation voltage exhibits a moderate scan rise time for the ion cluster per unit time, meaning the time required for the scanned voltage to cover the intermediate ion region is appropriate. This moderate scan rise time ensures that the sawtooth wave modulation voltage fully acts on the intermediate ions, effectively offsetting their velocity fluctuations, while preventing excessively fast scans from causing concentrated cooling force, or excessively slow scans from causing velocity deviations during cooling. This time characteristic precisely matches the velocity stability requirements of the intermediate ions, allowing the moderate cooling force to act continuously and smoothly on them, maintaining their longitudinal velocity close to the average cluster velocity and preventing the intermediate region from becoming a "fault zone" of velocity abrupt changes.

[0048] Based on the intermediate ion velocity data fed back by the cluster monitoring unit, the parameter control unit sends parameter control commands to the electron beam cooling unit, causing the electron beam cooling unit to output a sawtooth wave modulation voltage with a moderate absolute slope and moderate scan rise time. After being modulated by this voltage, the electron beam forms an energy gradient adapted to the intermediate ions within the cooling section of the storage ring, resulting in a gentle collision with the intermediate ions and generating a moderate cooling force. This moderate cooling force acts directionally on the longitudinal flight direction of the intermediate ions, only offsetting the excess velocity fluctuations caused by microscopic thermal motion, without changing their main flight velocity. This ensures that the intermediate ions maintain a stable longitudinal velocity, providing a smooth velocity transition basis for the deceleration of fast ions at the head and the acceleration or maintenance of slow ions at the tail. This, in turn, ensures the uniformity and regularity of the overall longitudinal density distribution of the ion cluster, supporting the eventual convergence to a narrowed Gaussian distribution. The entire control process is completed within the cooling section of the storage ring, without deflection magnetic field interference, ensuring that the moderate cooling force accurately and stably maintains the velocity of the intermediate ions.

[0049] According to an embodiment of the present invention, a weak cooling force is applied to the slow ions at the tail of the ion beam to maintain or increase the longitudinal velocity of the slow ions at the tail; the sawtooth wave modulation voltage corresponding to the weak cooling force has a small absolute slope, and the sawtooth wave modulation voltage has a long scan rise time for the ion beam per unit time.

[0050] Specifically, the weak cooling force control for the slow ions at the tail is precisely achieved through the sawtooth wave modulation voltage output by the electron gun of the electronic cooling device. Based on the slow ion velocity data and the overall density and morphology of the ion cluster fed back by the cluster monitoring unit, the electron gun outputs a modulation voltage with a small absolute slope, providing gentle energy support for the weak cooling force. The slow ions at the tail of the ion cluster are a group of ions lagging behind the average velocity during cyclic flight. Their longitudinal velocity is significantly lower than the average level of the cluster. If their velocity is not specifically controlled, they are prone to forming an excessive velocity difference with the head and middle ions, leading to widening of the longitudinal distribution or morphological distortion of the ion cluster. Applying a weak cooling force to the slow ions at the tail aims to prevent their velocity from decreasing further. Simultaneously, according to the overall control requirements of the ion cluster, their longitudinal velocity is appropriately increased, bringing the slow ion velocity closer to the average velocity of the cluster, reducing the longitudinal velocity difference within the ion cluster, and ensuring the uniformity of the cluster density distribution.

[0051] The generation of weak cooling force is directly related to the characteristics of the sawtooth wave modulation voltage. The corresponding sawtooth wave modulation voltage has a small absolute slope, and its amplitude change rate is much lower than that of strong and medium cooling forces, exhibiting a gradual change. This gradual slope causes the modulated electron beam to form a low-energy distribution in the slow ion region at the tail. When it collides gently with slow ions, the resulting directional deceleration force is weak and will not excessively cancel out the kinetic energy of the slow ions. This not only cancels out the velocity decay caused by microscopic thermal motion but also preserves enough kinetic energy for the slow ions to maintain their current velocity. Furthermore, under controlled conditions, the velocity can be increased through a slight push from the energy gradient. Simultaneously, the sawtooth wave modulation voltage with a small absolute slope allows the electron beam energy gradient to smoothly connect the tail and middle regions, ensuring a continuous and abrupt cooling force distribution along the entire length of the ion beam, preventing velocity fluctuations in the tail ions due to sudden changes in cooling force.

[0052] Complementing the small absolute slope, this sawtooth-wave modulation voltage has a long scan rise time for the ion beam per unit time, meaning the scan voltage has a longer time to cover the slow ion region at the tail. This long scan rise time provides ample buffer space for slow ion velocity adjustment, preventing insufficient application of the weak cooling force due to excessively fast scans, or a break in the velocity transition between tail and intermediate ions due to rapid velocity changes. This temporal characteristic precisely matches the velocity control requirements of slow ions, allowing the weak cooling force to act continuously and gently on the tail slow ions, gradually adjusting their longitudinal velocity: when the ion beam needs to converge, the weak cooling force maintains the slow ion velocity, preventing it from increasing the distance from the intermediate ions; when the ion beam needs to stretch, the weak cooling force moderately increases the slow ion velocity, pushing it to diffuse smoothly towards the outer edge of the beam tail, always maintaining velocity coordination with the intermediate ions.

[0053] Based on the slow ion velocity data at the tail and the overall density distribution of the ion bundle fed back by the bundle monitoring unit, the parameter control unit sends parameter control commands to the electron beam cooling unit, causing the electron beam cooling unit to output a sawtooth wave modulation voltage with a small absolute slope and a long scan rise time. After being modulated by this voltage, the electron beam forms a low-energy gradient adapted to the slow ions at the tail within the cooling section of the storage ring, resulting in a gentle collision with the slow ions and generating a weak cooling force. This weak cooling force acts directionally on the longitudinal flight direction of the slow ions at the tail, flexibly maintaining or moderately increasing the velocity according to the control requirements. This gradually converges the longitudinal velocity of the slow ions towards the average velocity of the bundle, effectively reducing the longitudinal velocity difference within the ion bundle. This, combined with the deceleration of the fast ions at the head and the velocity maintenance of the intermediate ions, forms a synergistic control, ensuring the regularity of the overall longitudinal density distribution of the ion bundle. The entire control process is completed in the cooling section of the storage ring, without deflection magnetic field interference, ensuring precise and stable velocity control of the slow ions at the tail by the weak cooling force, thus guaranteeing the final convergence of the ion bundle to a narrowed Gaussian distribution.

[0054] According to an embodiment of the present invention, when the sawtooth wave modulation voltage has a positive slope, the ion beam is stretched; when the sawtooth wave modulation voltage has a negative slope, the ion beam is compressed.

[0055] Specifically, the slope polarity of the sawtooth wave modulation voltage precisely controls the morphology of the ion beam through the electron gun of the electronic cooling device. Based on the ion beam density profile fed back by the ion beam monitoring unit, the electron gun switches between outputting a positive or negative slope modulation voltage, providing directional energy gradient support for ion beam stretching or compression. The slope polarity of the sawtooth wave modulation voltage directly determines the longitudinal control direction of the ion beam. Through precise correlation with the electron beam energy gradient, directional stretching or compression of the ion beam is achieved. Furthermore, this control process dynamically adapts to the density distribution requirements of the ion beam, ensuring that the ion beam ultimately converges to a narrowed Gaussian distribution.

[0056] When the sawtooth wave modulation voltage has a positive slope, its amplitude increases continuously with the sweep time, such as... Figure 3 Positive slope sawtooth wave sweep frequency period amplitude and sweep time As shown in the diagram, this voltage characteristic creates a longitudinal energy gradient in the electron beam output from the electron beam cooling unit, with a lower head and higher tail. The average energy of the electron beam is lower in the head region of the ion cluster and higher in the tail region, with the energy increasing monotonically from head to tail. In the figure, T represents the sweep frequency period. Based on this energy gradient, when ions and electrons undergo gentle collisions, the cooling force experienced by different positions in the ion cluster forms a corresponding gradient: the cooling force on the head ions is weaker, and the cooling force on the tail ions is stronger. This gradient distribution promotes moderate forward diffusion of head ions and accelerated follow-up of tail ions, thereby achieving longitudinal stretching of the ion cluster. This stretching effect effectively alleviates the problem of central ion density caused by an excessively narrow ion cluster, reduces beam scattering caused by mutual repulsion between ions, extends ion lifetime, and maintains the overall stability of the ion cluster, laying the foundation for subsequent precise control.

[0057] When the sawtooth wave modulation voltage has a negative slope, its amplitude decreases continuously with the sweep time, such as... Figure 2 Negative slope sawtooth wave sweep period amplitude and sweep time As shown in the diagram, the corresponding electron beam forms a longitudinal energy gradient with a high head and low tail. The average energy of the electron beam is higher in the head region of the ion cluster and lower in the tail region, with the energy decreasing monotonically from head to tail. Under the influence of this energy gradient, the gentle collisions between ions and electrons generate a directional cooling force: the fast ions at the head are subjected to a stronger cooling force, and their longitudinal velocity is rapidly reduced; the slow ions at the tail are subjected to a weaker cooling force, and their velocity is maintained or moderately increased. This differentiated cooling effect causes the head ions to decelerate and the tail ions to follow, gradually reducing the longitudinal distribution range of the ion cluster, achieving longitudinal compression. This compression can improve the problem of ion distribution dispersion caused by an excessively wide ion cluster, increase the brightness of the ion cluster, and make the longitudinal density distribution of the ion cluster more concentrated, meeting the requirements of physical experiments for concentrated ion beam distribution and small velocity differences. During this control process, the absolute value of the slope of the sawtooth wave modulation voltage is precisely matched with the intensity of strong / medium / weak cooling force and the short / medium / long scan rise time. Through the synergy of large / medium / small absolute slope values ​​and short / medium / long scan rise time, the accuracy of bundle morphology control is further improved.

[0058] Regardless of whether the sawtooth wave modulation voltage has a positive or negative slope, its control focus is on modulating the direction of the electron beam energy gradient through the voltage slope polarity, thereby guiding the longitudinal drift trend of the ions. Both voltage slopes follow the laws of sawtooth wave amplitude control and slope function; the amplitude and instantaneous frequency change continuously with the sweep time, and the absolute value of the slope can be flexibly adapted according to the envelope distribution of the ion beam, ensuring that the electron beam energy gradient completely covers the entire length of the ion beam. In actual control, the electron beam cooling unit automatically switches the slope polarity of the sawtooth wave modulation voltage based on the comparison between the actual length of the ion beam and the preset target length fed back by the beam monitoring unit. This allows the ion beam to gradually approach the target shape through dynamic control of stretching and compression, ultimately converging stably to a narrowed Gaussian distribution, achieving precise and efficient control of the longitudinal density of the ion beam.

[0059] The method of this invention significantly improves the uniformity and narrowing of the longitudinal density distribution of the ion beam by leveraging a differentiated cooling mechanism and dynamic parameter control strategy achieved through a sawtooth wave modulation voltage generated by the electron gun of the electronic cooling device. In practical applications, for cases where the ion beam is too narrow, longitudinal stretching is achieved through a positive slope sawtooth wave modulation voltage, alleviating the beam scattering problem caused by the density of central ions, reducing inter-ion repulsion, and extending ion lifetime and beam stability. For cases where the ion beam is too wide, longitudinal compression is achieved through a negative slope sawtooth wave modulation voltage, improving the dispersion of ion distribution and effectively increasing the brightness of the ion beam. The entire technical solution is simple in structure and highly efficient in control, requiring no complex additional hardware configuration, and can meet the stringent requirements for ion beam quality in particle physics experiments, nuclear physics research, and other fields, providing reliable technical support for related scientific research and application scenarios.

[0060] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for controlling the longitudinal density distribution of an ion beam in a storage ring, characterized in that, include: The actual length and longitudinal density distribution of the existing ion beam clusters within the storage ring are detected in real time, and the actual length of the ion beam clusters is compared with the preset target length to determine whether the longitudinal density distribution is too wide or too narrow. Based on the judgment result, a sawtooth wave modulation voltage is generated by the electron gun of the electronic cooling device, and an electron beam modulated by the sawtooth wave modulation voltage and matched with the velocity of the ion beam is emitted. The small relative velocity generated by the microscopic thermal motion between ions and electrons causes gentle collisions, and differential cooling is performed on the head, middle and tail of the ion beam to adjust the longitudinal velocity distribution of ions; wherein, the electron beam is modulated by the sawtooth wave modulation voltage to form a longitudinal energy gradient. Based on the real-time morphology of the ion beam cluster, the parameters of the sawtooth wave modulation voltage are continuously adjusted so that the longitudinal density distribution of the ion beam cluster converges to a narrow Gaussian distribution.

2. The method according to claim 1, characterized in that, The real-time detection of the actual length and longitudinal density distribution of the existing ion beam clusters within the storage ring, the emission of an electron beam modulated by the sawtooth wave modulation voltage and matched to the velocity of the ion beam clusters, and the occurrence of mild collisions are all performed in the cooling section of the electron cooling device within the storage ring.

3. The method according to claim 1, characterized in that, The direction of the sawtooth wave modulation voltage matches the longitudinal density distribution pattern of the ion beam: If the longitudinal density distribution of the ion beam is found to be too narrow, a sawtooth wave modulation voltage with a positive slope is used to make the electron beam form a longitudinal energy gradient with a low head and high tail, so as to stretch the ion beam. If the longitudinal density distribution of the ion beam is found to be too wide, a sawtooth wave modulation voltage with a negative slope is used to make the electron beam form a longitudinal energy gradient with a high head and low tail, so as to compress the ion beam.

4. The method according to claim 1, characterized in that, The differential cooling of the head, middle, and tail of the ion beam cluster to adjust the longitudinal velocity distribution of the ions specifically includes: By applying a continuously varying cooling force of different intensities to the fast ions at the head, the middle ions, and the slow ions at the tail along the entire length of the ion beam using the longitudinal energy gradient of the electron beam, the longitudinal velocity difference between the ions is adjusted, thereby controlling the ion beam to achieve aggregation or dispersion.

5. The method according to claim 4, characterized in that, A strong cooling force is applied to the head fast ions of the ion beam cluster to reduce the longitudinal velocity of the head fast ions; The sawtooth wave modulation voltage corresponding to the strong cooling force has a large absolute slope, and the sawtooth wave modulation voltage has a short scan rise time for the ion beam cluster per unit time.

6. The method according to claim 4, characterized in that, A moderate cooling force is applied to the intermediate ions of the ion beam cluster to maintain the longitudinal velocity of the intermediate ions; The sawtooth wave modulation voltage corresponding to the moderate cooling force has a moderate absolute slope, and the sawtooth wave modulation voltage has a moderate scan rise time for the ion beam cluster per unit time.

7. The method according to claim 4, characterized in that, A weak cooling force is applied to the slow ions at the tail of the ion beam cluster to maintain or increase the longitudinal velocity of the slow ions at the tail. The sawtooth wave modulation voltage corresponding to the weak cooling force has a small absolute slope, and the sawtooth wave modulation voltage has a long scan rise time for the ion beam cluster per unit time.

8. The method according to claim 5, 6 or 7, characterized in that, The sawtooth wave modulation voltage has a positive slope, and the ion beam is stretched. The sawtooth wave modulation voltage has a negative slope, and the ion beam is compressed.

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