Method for changing the number and energetic characteristics of laser pulse induced and accelerated particles

Abstract

The invention relates to a method for setting the quantity and energetic characteristics of particles induced and accelerated by a laser pulse, wherein a target is provided as a particle source and a laser pulse is generated whose full width at half maximum is at least 10% of the value of the central wavelength, - from the laser pulse, by modulation of the third derivative of the spectral phase (TOD) of the laser pulse, a prepulse defined by the target, the particle amount and particle energetic characteristics to be produced is generated in the vicinity of the laser pulse in such a manner that in case of negative TOD, a prepulse is generated and the temporal separation of the prepulse relative to the laser pulse and therewith the energy contained in the prepulse are increased to the required extent by raising the absolute value of the TOD of the laser pulse, - the second derivative of the spectral phase (GDD) of the laser pulse is modulated and the duration of the laser pulse is increased by raising the absolute value of the GDD, the essence of which is that the higher frequency components are arranged in the laser pulse in such a manner that in case of TOD with negative sign, the sign of the GDD is set to positive, then the electromagnetic wave packet formed by the laser pulse and the prepulse is delivered to the target.

Description

[0001] METHOD FOR CHANGING THE NUMBER AND ENERGETIC CHARACTERISTICS OF

[0002] LASER PULSE INDUCED AND ACCELERATED PARTICLES

[0003] The invention relates to a method for setting the quantity and energetic characteristics of particles induced and accelerated by a laser pulse, wherein a target is provided as a particle source and a laser pulse is generated.

[0004] One of the great advantages of laser particle acceleration over conventional accelerators is that in the focus of a laser pulse with short duration and therefore high intensity, it is possible to create an electromagnetic field that is orders of magnitude larger than the accelerating fields available in conventional accelerators. This would allow, for example, the 3 km long SLAC accelerator to be replaced by an about 10 cm long laser accelerator; that is, it would be possible to operate the laser accelerators in a much smaller space with less capital investment and at the same time with lower maintenance cost. Conventional accelerators, however, are still capable of generating much higher particle current and the accelerated particles are (quasi) monoenergetic. In contrast, known laser accelerators have a relatively broad spectral yield that decreases exponentially with higher particle energies.

[0005] According to the simplified basic scheme of laser particle acceleration, a high intensity laser pulse, i.e. a laser pulse of large electromagnetic field hits a target. The laser pulse produces plasma on the irradiated part of the target. The free electrons in the plasma are accelerated and expelled from the plasma by the electromagnetic field through some interaction. The interaction can be direct Coulomb explosion, or a much more complex process (e.g. so-called laser wakefield acceleration). The expelled electrons accelerate the ions within the plasma or a part of it by pulling them along due to the Coulomb force. In these cases, the whole physical process may be relatively simple (radiation pressure acceleration) or it may be the so-called target normal sheath acceleration (TNSA) involving also the surface impurity of the target, as it is known by the skilled person.

[0006] In addition to increasing the number and total energy of the accelerated particles, the major challenges of laser particle acceleration include the increase of maximum particle energy (cut-off energy) and shaping the energy spectrum towards a quasimonoenergetic shape. Research over the last few decades has shown that the number and the maximum energy of the accelerated particles depend on the material and the thickness of the target, and the laser pulse parameters. The latter includes the energy and the timing of prepulse(s) providing suitable preheating of the plasma.

[0007] For reasons of science history and experiment, parameter sets relating to electron and ion acceleration was treated separately for a long time. The central wavelength of existing high intensity lasers is around 1 pm. At this wavelength, electrons are typically accelerated in „underdense” materials, while ions are accelerated in „overdense” materials. The former refers to gases of ~ bar pressure, while the latter means solids and liquids. It is also known that a pulse structure is considered an ideal one for electron acceleration where the plasma is preheated to the required temperature before the main pulse by a prepulse or by the energy stored in the slower rising edge, while any prepulses mostly deteriorate the efficiency of ion acceleration. In case of the latter, it has also been found at the same time that the acceleration efficiency obtainable with a laser pulse being infinitesimally short (Dirac delta character) in time is small as compared to the one obtained by a pulse relatively slow rising edge in time. Relating to picosecond pulses, comprehensive joint research on electron and ion acceleration has been first conducted by an international group (R.A. Simpson et al., "Scaling of laser-driven electron and proton acceleration as a function of laser pulse duration, energy, and intensity in the multi-picosecond regime.", Phys. Plasmas 28, 013108 (2021)). As for femtosecond laser pulses, Pomerantz et al. have recently demonstrated in an ingenious experiment that it is possible to switch between electron and proton acceleration using the same experimental setup by varying merely the energy and timing of the prepulse (Cohen et al, Appl. Sci., 11 (2021) 5424). In other words, the number (as well as the type) of accelerated particles and their energetic characteristics can be changed by varying the parameters of the laser pulse.

[0008] According to state-of-the-art solutions, the required pulse structures are produced by optically separating a portion of the main pulse and making them lead in time relative to the main pulse using mechanical shifters. The needed energy ratios are set by energy filters. Such a procedure is described, for example, in the following publications: Cohen et al., Appl. Sci., 11 (2021) 5424, and D. Batani et al., Effects of laser prepulses on laser-induced proton generation, New J. Phys. 12 (2010) 045018. The main drawbacks of these solutions are that the energy of the laser pulse is reduced due to the losses necessarily accompanied with the separation, and expensive and complex equipment is required for the implementation.

[0009] When investigating the conditions of ion acceleration, several research groups have recently showed (e.g. Ziegler, T., et al. "Proton beam quality enhancement by spectral phase control of a PW-class laser system."; Loughran et al., Automated control and optimisation of laser-driven ion acceleration; A. Permogorov et al. "Effects of pulse chirp on laser-driven proton acceleration.") that it is possible to influence the energy of the accelerated ions by "chirping" of the pulse, i.e. by varying the second-order term of the spectral phase (Group Delay Dispersion — GDD) of the laser pulse. By increasing the absolute value of GDD, the laser pulse can be stretched in time, that results in an increase in the maximum energy of the accelerated particles and in the acceleration efficiency. It has also been observed that by changing the sign of the second -order term, the increase in efficiency is slightly asymmetric, i.e., greater with the stretching in one direction and slightly less in the other direction. This effect was assumed without no further specified reasons that the accelerating pulse duration would be already too short to have the capability to accelerate the expelled electrons at a longer distance. If the pulse were slightly longer in time, the charged particles would have stayed longer in the accelerating field. The reason of the slight asymmetry may be that, depending on the sign of the GDD, components of higher or lower optical frequency arrive at the target sooner. The GDD disperses the optical frequency components linearly in time in such a manner that in case of negative GDD, the higher frequency components, and in case of positive GDD, the lower frequency components lead. The higher frequency components are better absorbed in the target and make the plasma hotter than the lower frequency components do.

[0010] We found that by varying the third derivative of the spectral phase (Third Order Dispersion — TOD) of the laser pulse, energy can be rearranged — without optical separation — after the peak of the laser pulse from the laser pulse used for particle acceleration, which is hereinafter referred to as postpulse . Postpulse can be generated in case of positive TOD. It should be noted that the postpulse itself can be consisted of multiple smaller pulses, which collectively constitute the postpulse. According to our finding, by increasing the absolute value of the TOD, the temporal onset of the postpulse relative to the laser pulse can be increased within the laser pulse, as well as its magnitude.

[0011] It has further been found that by varying the TOD, the energy distribution within the laser pulse changes, but the total energy of the laser pulse is essentially unvaried; that is, more complex pulse structures can be generated practically without loss as compared to the separation techniques. Besides, the modulation of TOD requires a less complex optical assembly composed of equipment originally built into the majority of lasers, so the expenses are also lower than that of separation methods.

[0012] It has also been determined that the aforementioned GDD rearranges the optical frequency components of the laser pulse linearly in time, such that, in the case of negative GDD, the higher frequency components are located at the front. We found that the TOD changes the temporal sequence of the spectral components with just the opposite sign, and what is more important, nonlinearly in time. Thus, by adjusting the TOD and GDD precursors accordingly, the temporal shape of the laser pulse can be changed essentially arbitrarily. For example, the leading edge can be made steeper. Furthermore, the spectral distribution between the prepulse and the laser pulse can also be modified in this way, so that the higher frequency components are positioned at the front of the laser pulse and the lower frequency components at the end of the laser pulse (i.e. the postpulse mentioned above). This results in the electrons reaching their desired energy (temperature) more rapidly and detach from the atomic nuclei, that is, the electron cloud composed of high energy electrons forms more quickly, then the electrons can be better accelerated by the "red", lower frequency components rearranged into the longer duration postpulse. In the end, the acceleration efficiency increases.

[0013] It is also recognized that the more effective the method of the invention, the higher the temporal intensity contrast of the laser pulse (in particular the incoherent contrast) and the broader the spectrum (i.e. the shorter the laser pulse). For the sake of broader spectrum, a laser pulse is generated whose full width at half maximum is at least 10% of the value of the central wavelength. The temporal (intensity) contrast, or signal -to-noise ratio, is composed of two parts: the coherent and the incoherent contrast. Coherent contrast is expressed as the quotient of the postpulse and laser pulse intensity. Incoherent contrast is defined as the quotient of the maximum intensity of other background photon noise (e.g. amplified spontaneous emission, parametric superfluorescence) and the peak intensity, as it is known by the skilled person. In case of high peak intensity laser systems, the aim is to keep especially the latter at sufficiently low level, since the non-coherent noise lasts as long as the duration of the so-called pump pulse, which may be several nanoseconds as well. That is to say, although the intensity is low, but the energy involved may be considerable.

[0014] It has further been found that the energetic characteristics of the accelerated particles (the energy of the highest energy particle (cutoff energy) and the energy of the total particle pulse) can be optimized separately with GDD and TOD having different absolute values.

[0015] The aim of the invention is to create a method for setting the quantity and energetic characteristics of laser pulse induced and accelerated particles that is free from the drawbacks of the state-of-the-art solutions. In particular, the aim of the invention is to provide a method wherein the required pulse structure is produced not by optical separation, but by modulation of the TOD and the GDD of the laser pulse, and wherein the higher frequency components are arranged to be at the front of the main pulse and the lower frequency components are arranged to be in the postpulse, as a result of which the efficiency of particle acceleration can be increased.

[0016] The problem was solved according to the invention by a method wherein a target is provided as a particle source and a laser pulse is generated. By modulation of the third derivative of the spectral phase (TOD) and the second-order term of the spectral phase (GDD) of the laser pulse, a pulse structure is generated from the laser pulse that corresponds to the target, the type, amount and energetic characteristics of the particle to be produced, wherein the higher frequency components are arranged to be at the front of the laser pulse and the lower frequency components are arranged to be in the postpulse following the laser pulse.

[0017] The essence of the invention is that by using the method:

[0018] - the higher-frequency components of the laser pulse are shifted to the front of the laser pulse by setting the sign of the GDD of the laser pulse to negative, and then

[0019] - choosing TOD to be positive by varying the optical frequencies quadratically creates a specifically lower optical frequency and time-delayed postpulse, while also sharpening the slope of the leading edge by forward-shifting the higher frequency components;

[0020] - the temporal separation of the prepulse relative to the laser pulse and therewith the energy contained in the postpulses are increased to the required extent by raising the absolute value of the TOD of the laser pulse, - the electromagnetic wave packet formed by the entire pulse structure is delivered to the target.

[0021] Certain preferred embodiments of the invention are defined in the dependent claims.

[0022] Further details of the invention will be disclosed by means of embodiments and drawings.

[0023] In Figure 1, a transformation-limited laser pulse (GDD = 0 fs2, TOD = 0 fs3) is seen,

[0024] Figure 2a shows the effect of GDD alone on the temporal shape of the laser pulse in case of GDD = -700 fs2and TOD = 0 fs3,

[0025] Figure 2b shows the effect of GDD alone on the temporal shape of the laser pulse in case of GDD = 800 fs2and TOD = 0 fs3,

[0026] Figure 3 shows the effect of TOD alone on the temporal shape of the laser pulse in case of GDD = 0 fs2and TOD = +20000 fs3,

[0027] Figure 4a shows the maximum and total energy of the laser pulse induced particles for various GDD values of the laser pulse in case of TOD = 0 fs3,

[0028] Figure 4b shows the maximum and total energy of the laser pulse induced particles for various GDD and TOD values of the laser pulse.

[0029] The invention relates to a method for setting the quantity and energetic characteristics of laser pulse induced and accelerated particles, wherein a target is provided as a particle source and a laser pulse is generated. Preferably, a transformation-limited laser pulse is generated as the laser pulse, whose length expressed in full width at half maximum is preferably up to five optical cycles. It is noted that, application of longer laser pulses may optionally be considered as well, but the full width at half maximum of the laser pulse used in the method according to the invention is at least 10% of the value of the central wavelength. In the context of the present invention, the target can be any per se known object of solid, liquid or gaseous state of matter commonly used in laser particle accelerations, as it is known by the skilled person.

[0030] In the context of the present invention, "setting the quantity of particles" is understood as meaning that by varying the laser pulse properties hereafter presented, it can be controlled that approximately how much particles of a given type are to be produced, and in what proportion the different types of particles are to be produced when various types are being induced in the method. Furthermore, "setting the energetic characteristics of particles" is understood as meaning that by setting the properties of the laser pulse — evidently within a certain range — , it can be controlled that how much the total energy, the maximum energy of the laser pulse induced and accelerated particles, and what the energy spectrum shape are to be.

[0031] In the method according to the invention, by modulation of the third derivative of the spectral phase (TOD) of the laser pulse, a pulse structure is generated from the laser pulse that defined by the target, the particle amount and particle energetic characteristics to be produced. In other words, by setting the TOD of the laser pulse, a postpulse is generated from the laser pulse by means of which — within reasonable limits — particles of approximately the required amount and energetic characteristics can be produced from the target. The postpulse and the laser pulse form an electromagnetic wave packet (pulse structure) together. Preferably, the postpulse and the laser pulse overlap each other partially.

[0032] "Modulation of the TOD of the laser pulse" is understood as meaning the changing of the sign and magnitude (absolute value) of the TOD, the setting to a required value. In the method:

[0033] - choosing the value of TOD to be positive, a postpulse is generated,

[0034] - the temporal separation of the prepulse relative to the laser pulse and therewith the energy contained in the postpulses are increased to the required extent by raising the absolute value of the TOD of the laser pulse,

[0035] - the higher frequency components of the laser pulse are arranged in the prepulse in such a way that in case of negative sign of the TOD of the laser pulse, the sign of the GDD of the laser pulse is set to positive, then

[0036] - the electromagnetic wave packet formed by the prepulse and the laser pulse is delivered to the target.

[0037] In the method according to the invention, also the second derivative of the spectral phase (GDD) of the laser pulse is modulated in addition to the modulation of the TOD; consequently, it is possible to produce more precisely particle or particles of a given type, being typical of the target, in the needed amount and with the required energetic characteristics. For example, by increasing the absolute value of the GDD, the duration of the laser pulse can be increased; thus, the postpulse can be separated by increasing the TOD. Figure 1 shows a transformation-limited laser pulse with a full width at half maximum of 13.4 fs. Figure 2a shows the normalized intensity curve of a laser pulse with an increased absolute value of its GDD. As it is observed, the length (duration) of the laser pulse is increased. Further increasing the absolute value of the GDD results in an increase in the length of the laser beam, as it is seen in Figure 2b. A consideration of Figures 2a and 2b reveals that the slopes of the rising edges do not vary with the sign, but rather with the value of the GDD.

[0038] Figure 3 shows the effect of TOD alone on the temporal shape of the laser pulse. To eliminate the effect of GDD, the value of GDD was chosen to be zero. The TOD rearranges the frequency components quadratically, i.e. one side of the electromagnetic wave packet becomes steeper and the other side becomes more elongated. As it is seen in Figure 3, in the case of positive TOD, the postpulse is generated by rearranging the energy of the laser pulse, whose intensity is lower than that of the laser pulse. At the same time, the higher frequency components make the rising edge of the pulse steeper.

[0039] By changing the signs and values of the TOD and the GDD, not only the intensity profde of the laser pulse can be modified but also the distribution of its frequency components. The GDD rearranges the frequency components of the laser pulse linearly so that in case of a GDD with a negative sign, the higher frequency components are positioned at the front considering the direction of propagation of the laser pulse. In the method according to the invention, the higher frequency components of the laser pulse are arranged at the front of the pulse in such a way that in case of the TOD of the laser pulse has positive sign, the sign of the GDD of the laser pulse is set to negative. By rearranging the frequency components, the two main parts of the ion acceleration can be optimized. The two main parts are as follows: i.) ionization of the dense target and heating of the electrons in the plasma; ii) acceleration of the electron cloud and the ion cloud binding to it by the Coulomb force. The absorption of the material is higher for the higher frequency — "blue" — components in the prepulse; therefore, the electrons heat up fast to the required energy (temperature) and detach from the nuclei; that is, the electron cloud composed of high energy electrons forms more quickly. At the same time, the plasma expands during the plasma formation, resulting in a decrease in particle density and, consequently, a reduction in the absorbed energy, as well. In other words, the prepulse has to be suitably short to prevent appreciable expansion. Then the formed electron cloud is accelerated by the lower frequency — "red" — components that are rearranged into a longer laser pulse following the prepulse. The reason is that the ponderomotive force of the electromagnetic field acting on the charged particles is inversely proportional to the square of the frequency of the electromagnetic field (i.e. directly proportional to the square of the wavelength). During acceleration, the ponderomotive effect is preferable, i.e., the acceleration can last longer due to the ponderomotive effect and the length of the pulse portion.

[0040] In a particularly preferred embodiment, the spectral phase of the laser pulse is expanded in Taylor series and the TOD of the laser pulse is changed by varying the value of the expansion coefficient belonging to the third-order derivative of the expansion, and the GDD of the laser pulse is changed by varying the value of the expansion coefficient belonging to the second-order derivative of the expansion. The modulation of the third derivative of the spectral phase (TOD) and the second order term of the spectral phase (GDD) of the laser pulse is implemented preferably by means of a per se known acousto -optical programmable dispersive filter (AOPDF). In another possible embodiment, the modulation of the third derivative of the spectral phase (TOD) and the second order term of the spectral phase (GDD) of the laser pulse is implemented by varying the angles of incidence of prisms functioning as dispersive elements and / or by appropriately choosing the apex angle of prisms, as the skilled person will understand. In a further possible embodiment, the modulation of the third derivative of the spectral phase (TOD) and the second order term of the spectral phase (GDD) of the laser pulse is implemented by varying the angles of incidence of gratings functioning as dispersive elements and / or by appropriately choosing the number of grooves of gratings. Optionally, the modulation of the third derivative of the spectral phase (TOD) and the second order term of the spectral phase (GDD) of the laser pulse is implemented by means of chirped mirrors functioning as dispersive elements and / or by means of other polarization and dispersion optical elements.

[0041] The laser pulse shape containing the prepulse and corresponding to the given target, the particle amount and the particle energetic characteristics to be produced is determined experimentally or by simulation. In a possible embodiment, several laser pulses are generated in succession, which are focused on a target that can be renewed shot by shot. Preferably, the target is a liquid target. The incoherent contrast of the laser pulses is chosen to be the highest possible . Particles leaving the target are detected using a Thomson ion spectrometer. This can be used to record the energy spectrum of accelerated ions (it is a kind of charge-to-mass ratio spectrometer). In this embodiment, the liquid jet target system is operated with heavy water, and the thickness of the liquid sheet is 300 nm. The Thomson ion spectrometer is used to determine the spectrum of the accelerated deuteron ions shot by shot. It should be noted that alternative types of targets (e.g. solid or gaseous) or materials can be used to induce and accelerate different types of particles, as is obvious to the skilled person. In this embodiment, AOPDF is used to vary the magnitude and sign of the GDD and TOD of the laser beam for each laser pulse separately, while the maximum energy of the deuteron ions and the total energy of the deuteron pulses are measured for each acceleration. The results of such a scanning are shown in Figures 4a and 4b. The highest energy deuterons produced during the accelerations belonging to the various values of GDD (see below) and TOD (see above) are represented by blue dots, whose values expressed in MeV can be read from the left vertical axis, while the total energy of the particles produced during each acceleration are represented by yellow dots, whose values expressed in mJ can be read from the right vertical axis. Figure 4a shows the result of a scanning where only the GDD values of the laser pulses were varied (TOD = 0). It can be seen that the highest energy deuterons were produced at GDD = -600 fs2and, at the same time, deuteron pulses of the highest total energy were measured at GDD = -200 fs2. Therefore, either the maximum energy of the particles or the total energy of the particles can be maximized by varying the GDD. In Figure 4b, both the GDD (black, below) and the TOD (red, above) of the laser pulses were varied. In this case, the deuteron pulses of the highest total energy were detected at GDD = -700 fs2, within which the highest energy deuterons were measured at TOD = 10000 fs3. That is, by varying both TOD and GDD, the maximum energy of the deuterons and the total energy of the particles can be maximized.

[0042] It is clear that a skilled person may find alternative solutions to embodiments disclosed herein, which, however, fall within the scope of the invention defined by the claims.

Claims

CLAIMS1. Method for setting the quantity and energetic characteristics of particles induced and accelerated by a laser pulse wherein a target is provided as a particle source and a laser pulse is generated the full width at half maximum of which is at least 10% of the value of the central wavelength,- from the laser pulse, by modulation of the third derivative of the spectral phase (TOD) of the laser pulse, a prepulse defined by the target, the particle amount and particle energetic characteristics to be produced is generated in the vicinity of the laser pulse in such a manner that in case of negative TOD, a prepulse is generated and the temporal separation of the prepulse relative to the laser pulse and therewith the energy contained in the prepulse are increased to the required extent by raising the absolute value of the TOD of the laser pulse,- the second derivative of the spectral phase (GDD) of the laser pulse is modulated and the duration of the laser pulse is increased by raising the absolute value of the GDD, characterized in that the higher frequency components are arranged in the laser pulse in such a manner that in case of TOD with negative sign, the sign of the GDD is set to positive, then the electromagnetic wave packet formed by the laser pulse and the prepulse is delivered to the target.

2. The method according to Claim 1, characterized in that a transformation-limited laser pulse is generated as the laser pulse.

3. The method according to Claim 1 or 2, characterized in that the laser pulse and the prepulse partially overlap.

4. The method according to any one of Claims 1 to 3, characterized in that the spectral phase of the laser pulse is expanded in Taylor series and the TOD of the laser pulse is changed by varying the value of the expansion coefficient belonging to the third-order derivative of the expansion, and preferably, the GDD of the laser pulse is changed by varying the value of the expansion coefficient belonging to the second-order derivative of the expansion.

5. The method according to any one of Claims 1 to 4, characterized in that the laser pulse shape having a prepulse defined by the given target, the particle amount and the particle energetic characteristics to be produced is determined experimentally or by simulation.

6. The method according to any one of Claims 1 to 5, characterized in that the energetic characteristics of the particles are selected from the group consisting of total energy, maximumparticle energy and shape of energy spectrum of the laser pulse induced and accelerated particles.

7. The method according to any one of Claims 1 to 5, characterized in that the incoherent contrast of the laser pulse is chosen to be the highest possible.

8. The method according to any one of Claims 1 to 7, characterized in that the length of the laser pulse is 15 fs at longest.

9. The method according to any one of Claims 1 to 8, characterized in that the modulation of the third derivative of the spectral phase (TOD) and the second order term of the spectral phase (GDD) of the laser pulse is implemented by means of a per se known acousto -optical programmable dispersive fdter (AOPDF).

10. The method according to any one of Claims 1 to 8, characterized in that the modulation of the third derivative of the spectral phase (TOD) and the second order term of the spectral phase (GDD) of the laser pulse is implemented by varying the angles of incidence of prisms functioning as dispersive elements and / or by appropriately choosing the apex angle of prisms.

11. The method according to any one of Claims 1 to 8, characterized in that the modulation of the third derivative of the spectral phase (TOD) and the second order term of the spectral phase (GDD) of the laser pulse is implemented by varying the angles of incidence of gratings functioning as dispersive elements and / or by appropriately choosing the number of grooves of gratings.

12. The method according to any one of Claims 1 to 8, characterized in that the modulation of the third derivative of the spectral phase (TOD) and the second order term of the spectral phase (GDD) of the laser pulse is implemented by means of chirped mirrors functioning as dispersive elements and / or by means of other polarization and dispersion optical elements.

13. The method according to any one of Claims 1 to 12, characterized in that the target is in a solid, liquid or gaseous state.

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