Wakefield Amplitude Research Articles

THz radiation generation from plasma wakefield driven by skew-cosh-Gaussian laser beam under an undulator magnetic field

The paper examines theoretically the generation of terahertz (THz) radiation as a result of wakefields generated by skew-cosh-Gaussian (skew-chG) laser beam propagating in collisional plasma under an undulator magnetic field. Analytical and non-linear equations have been derived to describe the generation of THz radiation by skew-chG laser beam. Using equations of motion, continuity equations, and perturbation technique, the transverse and longitudinal wakefield has also been derived in the presence of an undulator magnetic field. It is shown that the collisional plasma carries a higher longitudinal wakefield amplitude while the undulator amplitudes are lower. In addition, it is found that smaller collision frequencies make larger wakefield amplitudes that generate terahertz radiation. However, when the collision frequency becomes equal to the plasma frequency, the wakefield amplitude is greatly reduced. Moreover, it is observed that the THz field decreases with the increase of the beam waist of the skew-chG laser beam. It is also shown that the THz field exhibits an increasing behavior with increasing s parameter and undulator amplitudes despite the presence of significant collisions.

Excitation of wakefields in carbon nanotubes: a hydrodynamic model approach

The interactions of charged particles with carbon nanotubes (CNTs) may excite electromagnetic modes in the electron gas produced in the cylindrical graphene shell constituting the nanotube wall. This wake effect has recently been proposed as a potential novel method of short-wavelength high-gradient particle acceleration. In this work, the excitation of these wakefields is studied by means of the linearized hydrodynamic model. In this model, the electronic excitations on the nanotube surface are described treating the electron gas as a 2D plasma with additional contributions to the fluid momentum equation from specific solid-state properties of the gas. General expressions are derived for the excited longitudinal and transverse wakefields. Numerical results are obtained for a charged particle moving within a CNT, paraxially to its axis, showing how the wakefield is affected by parameters such as the particle velocity and its radial position, the nanotube radius, and a friction factor, which can be used as a phenomenological parameter to describe effects from the ionic lattice. Assuming a particle driver propagating on axis at a given velocity, optimal parameters were obtained to maximize the longitudinal wakefield amplitude.

Development of the self-modulation instability of a relativistic proton bunch in plasma

Self-modulation is a beam–plasma instability that is useful to drive large-amplitude wakefields with bunches much longer than the plasma skin depth. We present experimental results showing that, when increasing the ratio between the initial transverse size of the bunch and the plasma skin depth, the instability occurs later along the bunch, or not at all, over a fixed plasma length because the amplitude of the initial wakefields decreases. We show cases for which self-modulation does not develop, and we introduce a simple model discussing the conditions for which it would not occur after any plasma length. Changing bunch size and plasma electron density also changes the growth rate of the instability. We discuss the impact of these results on the design of a particle accelerator based on the self-modulation instability seeded by a relativistic ionization front, such as the future upgrade of the Advanced WAKefield Experiment.

Flying focus laser Wakefield scheme for efficient acceleration

The acceleration of charged particles with a short laser pulse is a revolutionary acceleration technology, but many restrictions limit their advantages. Wave breaking and dephasing are most important of these restrictions which weaken acceleration efficiency in the laser Wakefield acceleration scheme. The purpose of this paper is to demonstrate that flying focus laser Wakefield acceleration (FF-LWFA) can confirm this effectiveness. Flying focus creates in the focal region of a hyper-chromatic lens when the chirped laser pulse passing through them. Therefore, by controlling the lens chromaticity and initial chirp characteristics, the focal point velocity can be controlled and adjusted near the speed of light. For a realistic working parameter, two-dimensional simulation results show the flying focus pulse can retain its shape and energy within a few centimeters (one order of magnitude greater than Rayleigh's length). We introduce a velocity interval around velocity of light in which dephasing and wave breaking are restricted and high acceleration gradients (about a hundred of GeV/m) are achieved in the flying focus region. Moreover, in the optimized condition for negative chirp, wakefield amplitude is increased 50 %. Under this ideal situation, 0.5 % of background electrons accelerate to 2GeV in the 5 cm, where the acceleration gradient reaches to, 40GeV/m, and about 0.2 % of them accelerate up to 10GeV.

Electron acceleration by wakefield generated by the propagation of chirped laser pulse in plasma

A study of generation of wakefield and particle acceleration via propagation of linearly polarised, chirped, Gaussian laser pulse in preformed plasma channel is presented. Perturbation technique is used to separate slow and fast varying plasma electron velocities and density. Considering the laser pulse length and amplitude to be evolving along the propagation distance, nonlinear fluid equations are used to derive longitudinal electric wakefields at varying propagation distances for chirped as well as unchirped pulses. It has been seen that longitudinal wakefield amplitude generated by positively (negatively) chirped laser pulses is higher (lower) than the amplitude obtained by unchirped laser pulses. The wakefield amplitudes are optimized with respect to the propagation distance. Further, trapping and acceleration of electrons by the generated wakes, is analysed. Comparing the energy of an accelerated test electron using chirped and unchirped laser pulses, it is shown that positively chirped laser pulses are capable of accelerating test electron to maximum energy using minimum injection energy. Hence, highest energy gain can be obtained by propagation of positively chirped laser pulse in plasma.

Numerical study of electron acceleration driven by two-color laser pulses

The use of two-color relativistic femtosecond laser pulses for large-amplitude wakefield excitation and electron acceleration to relativistic energies in very short distances is a promising candidate that has recently been investigated experimentally and numerically by using the particle-in-cell method. Here, we have numerically studied the evolution of a large-amplitude wakefield excited by two-color relativistic femtosecond laser pulses in an underdense plasma. Moreover, the effects of some physical parameters such as two-color pulse polarization and time delay on the wakefield, and the electron acceleration are investigated. The results show that the wakefield amplitude and the energy of the accelerated electrons can be controlled by these parameters. We compare some results with those obtained by applying single-color pulses with similar energy. According to the comparison results, by applying two-color laser pulses, a stronger wakefield and higher electron energies can be obtained. We also show that our results are in good agreement with the experimental data obtained earlier.

Role of solar wind on the ionic escaping from Venus upper ionosphere via plasma wakefield

According to the observations that detected significant ionospheric escape from Venus, a test charge approach is suggested to explain the ionic loss caused by the solar wind (SW) interaction with the Venusian upper ionosphere. The proposed plasma system consists of two positive planetary ions (H + and O +) with isothermal electrons and streaming SW protons, with Maxwellian electrons. The electrostatic Debye screening and wakefield potentials caused by a moving test charge as well as the modified dielectric constant of the ion-acoustic waves (IAWs) created in the model are derived. The normalized Debye potential is found to decrease exponentially with the axial distance. Whereas the amplitude of the wakefield potential is amplified with the altitudes and decreases with increasing the density of either planetary oxygen or the SW protons but it is enhanced by SW electrons number density. However, the wakefield amplitude is not affected by the SW protons velocity or their temperatures because the SW protons velocity is fast compared with the velocity of the plasma system. Thus, the properties of the ions escaping are affected by the velocity variations within a certain range called the velocity scale window. The obtained results are found to be in a good agreement with the observed data.

Impact of wiggler magnetic field on wakefield generation and electron acceleration by Gaussian, super-Gaussian and Bessel–Gaussian laser pulses propagating in collisionless plasma

In this research, the process of electron acceleration and wakefield generation by Gaussian-like (GL), super-Gaussian (SG) and Bessel–Gaussian (BG) laser pulses through cold collisionless plasma in the presence of a planar magnetostatic wiggler are studied. Three different types of laser spatial profiles, GL, SG and BG, are considered. Additionally, using the hydrodynamics fluid equations, Maxwell's equations as well as the perturbation technique for GL, SG and BG laser pulses in the weakly nonlinear regime and in the presence of a planar magnetostatic wiggler, governing equations for analysing the laser wakefield and electron acceleration have been derived and compared correspondingly. In addition, the effect of some important factors, including the wiggler field strengths, laser intensity, pulse length, plasma electron density and laser frequency on the wakefield and the electron energy gain, have been investigated. Numerical results show that enhancing the wiggler magnetic field results in an increase in the amplitude of the wakefield. Furthermore, it is observed that in comparison with the wakefield amplitude excited by SG and GL laser pulses, the amplitude of the wakefield excited by BG laser pulse is larger when the wiggler field is enhanced. Moreover, it is realized that the type of the laser profile, selected laser parameters and wiggler magnetic field are the most decisive and effective factors in the wakefield amplitude and shape of wakefield generation through cold collisionless plasma. Also, it is seen that as the pulse length declines, the amplitude of the wakefield increases, and correspondingly the resonance positions shift to higher ${({\varOmega _w}/{\varOmega _p})_{max}}$ values.

Generation of THz radiation by wakefield under a wiggler magnetic field: An analytical study

In this article, the generation of terahertz (THz) radiation owing to wakefields produced by Gaussian-like laser pulse propagating throughout magnetized plasma has been investigated analytically under a wiggler magnetic field. Non-linear equations and analytical formulations governing the laser pulse THz radiation generation at a mildly relativistic regime have been derived. Besides, the total electric and magnetic wakefields inside and behind the laser pulse by employing the relativistic equations of motion, Maxwell’s equations, and perturbation technique in the attendance of a planar magnetostatic wiggler have been obtained. It is shown that the maximum transverse electric wakefield amplitude has an increasing trend with enchanting the wiggler frequency for inside and behind the laser pulse and the peak of the maximum transverse electric wakefield amplitude behind of laser pulse is higher compared to the inside of laser pulse for different values of the wiggler magnetic field. Furthermore, it is observed that electric wakefield amplitude has a fluctuating behavior inside and behind the laser pulse due to the existence of the planar magnetostatic wiggler. Also, it is shown that by using a wiggler magnetic field and components of perturbed velocities, we can generate THz waves. Moreover, it is found that we can achieve the needed values of the wiggler magnetic field for THz radiation generation for different values of the laser strength parameters. Indeed, we can control the generation of THz radiation throughout magnetized plasma by adjusting the wiggler magnetic field and laser pulse intensity.

Controlling the characteristics of injected and accelerated electron bunch in corrugated plasma channel by temporally asymmetric laser pulses

In laser-driven plasma wakefield accelerators, the accelerating electric field is orders of magnitude stronger than in conventional radio-frequency particle accelerators, but the dephasing between the ultrarelativistic electron bunch and the wakefield traveling at the group velocity of the laser pulse puts a limit on the energy gain. Quasi-phase-matching, enabled by corrugated plasma channels, is a technique for overcoming the dephasing limitation. The attainable energy and the final properties of accelerated electron beams are of utmost importance in laser wakefield acceleration (LWFA). In this work, using two-dimensional particle-in-cell simulations, the effect of the driving pulse duration on the performance of quasi-phase-matched laser wakefield acceleration (QPM-LWFA) is investigated. It is observed that for a pulse duration around half the plasma period, the maximum energy gain of the beam electrons finds its peak value. However, the results show that for a pulse of that duration the collimation of the bunch is much worse, compared to the case where the pulse duration is twice as long. Furthermore, the dynamics of the laser pulse and the evolution of the quality of the externally-injected electron bunch are studied for a symmetric pulse with sine-squared temporal profile, a positive skew pulse (i.e., one with sharp rise and slow fall), and a negative skew pulse (i.e., one with a slow rise and sharp fall). The results indicate that for a laser pulse with an appropriate pulse length compared with the plasma wavelength, the wakefield amplitude can be greatly enhanced by using a positive skew pulse, which leads to higher energy gain. Initially, this results from the stronger ponderomotive force associated with a fast rise time. Later, due to the distinct evolution of the three pulses with different initial profiles, the wakefield excited by the positive skew pulse becomes even stronger. In our simulations, the maximum energy gain for the asymmetric laser pulse with a fast rise time is almost two times larger than for the temporally symmetric laser pulse. Nevertheless, stronger focusing and defocusing fields are generated as well if a positive skew pulse is applied, which degrade the collimation of the bunch. These results should be taken into account in the design of miniature particle accelerators based on QPM-LWFA.

Magnetic field-assisted wakefield generation and electron acceleration by Gaussian and super-Gaussian laser pulses in plasma

This study focuses on electron acceleration and wakefield produced by Gaussian and Super-Gaussian (SG) laser pulses through plasma medium in the attendance of an external magnetic field. Two shapes of different laser spatial profiles Gaussian and SG are considered. Besides, governing equations for analysis of laser wakefield and electron acceleration by using of hydrodynamics fluid equations, Maxwell’s equations and perturbation technique for Gaussian and SG laser pulses in weakly nonlinear regime have been derived. In addition, influence of the external magnetic field strengths, laser intensity, the pulselength, the plasma electron density and the laser frequency on the wakefield and the electron energy gain have been investigated. Numerical results indicate that by increasing of external magnetic field, the amplitude of wakefield increases. Moreover, it is observed that wakefield amplitude excited by SG laser pulse in comparison with Gaussian laser pulse is larger when external magnetic field is increased. Furthermore, it is found that wakefield amplitude and shape of wakefield generation in within homogeneous plasma greatly are related to the laser profile type, selected laser parameters and external magnetic field. In addition, it is seen that influence of external magnetic field, while laser intensity enhances, on the electron energy gain in SG and Gaussian laser pulses is insignificant.

Witness electron beam injection using an active plasma lens for a proton beam-driven plasma wakefield accelerator

An active plasma lens focuses the beam in both the horizontal and vertical planes simultaneously using a magnetic field generated by a discharge current through the plasma. A beam size of 5--10 $\mu$m can be achieved within a short distance using a focusing gradient on the order of 100 T/m. The active plasma lens is therefore an attractive element for plasma wakefield acceleration, because an ultra-small size of the witness electron beam is required for injection into the plasma wakefield to minimize emittance growth and to enhance the capturing efficiency. When the drive beam and witness electron beam co-propagate through the active plasma lens, interactions between the drive and witness beams, and the plasma must be considered. In this paper, through particle-in-cell simulations, we discuss the possibility of using an active plasma lens for the final focusing of the electron beam for the AWAKE RUN 2 experiments. It is confirmed that the amplitude of the plasma wakefield excited by proton bunches remains the same even after propagation through the active plasma lens. The emittance of the witness electron beam increases rapidly in the plasma density ramp regions of the lens. Nevertheless, when the witness electron beam has a charge of 100 pC, emittance of 10 mm mrad, and bunch length of 60 $\mu$m, its emittance growth is not significant along the active plasma lens. For small emittance, such as 2 mm mrad, the emittance growth is found to be strongly dependent on the RMS beam size, plasma density, and multiple Coulomb scattering.

DEPENDENCE OF WAKEFIELD EXCITATION IN PLASMA BY NON-RESONANT SEQUENCE OF ELECTRON BUNCHES ON THEIR LENGTHS

The present paper describes the results of numerical simulation (using 2d3v code LCODE) of the regime, when the wakefield is excited at maximum growth rate in the plasma by a nonresonant sequence of relativistic electron bunches. As a result, the wakefield increases approximately in steps. The paper gives the parameters, at which this regime is achieved. It is shown that for smaller bunch radii, the amplitude of the excited wakefield is larger. At long lengths of the bunches, the amplitude of the wakefield is larger, in contrast to the excitation by the resonant sequence of bunches.

Resonant excitation of very high gradient plasma wakefield accelerators by optical-period bunch trains

Using a periodic electron beam bunch train to resonantly excite plasma wakefields in the quasi-nonlinear (QNL) regime has distinct advantages over employing a single, higher charge bunch. Resonant excitation in the QNL regime can produce plasma electron blowout using very low emittance beams with a small charge per pulse: the local density perturbation is extremely nonlinear, achieving total rarefaction, yet the resonant response of the plasma electrons at the plasma frequency is preserved. Such a pulse train, with inter-bunch spacing equal to the plasma period, can be produced via inverse free-electron laser bunching. To achieve resonance with a laser wavelength of a few microns, a high plasma density is used, with the attendant possibility of obtaining extremely large wakefield amplitude, near 1 TV/m for FACET-II parameters. In this article, we use particle-in-cell simulations to study the plasma response, the beam modulation evolution, and the instabilities encountered, that arise when using a bunching scheme to resonantly excite waves in a dense plasma.

The Effect of Chirped Gaussian Laser Pulse on the Acceleration of Plasma Electrons in a Plasma Wakefield Accelerator in the Presence of a Planar Undulator Field

Improving the acceleration process in a very compact structure by using laser-plasma interactions has attracted various researchers’ attention in recent years. Novel ideas, technologies, and comprehensive development in the relevant physics enabled the expansion of plasma wakefield accelerators. In this study, the energy gain and acceleration of electrons in the plasma medium have been investigated through the wakefield generated by a chirped Gaussian laser pulse in the presence of a planar magnetic undulator field. The fourth-order Runge–Kutta method was applied to simulate the wakefield and to determine the electron energy gain. In order to improve the oscillatory velocity of electrons in a laser-plasma accelerator, a planar undulator magnetic field was used. The numerical results indicated that with increasing undulator field strength, the wakefield amplitude and the electron energy gain increased noticeably. In addition, increasing the undulator wavelength for constant values of the undulator field strength leads to an increase in the wakefield amplitude and electron energy gain. Further results revealed an optimized value of chirped parameter, in which the wakefield amplitude and the electron energy gain could be maximum.

Transition between Instability and Seeded Self-Modulation of a Relativistic Particle Bunch in Plasma.

We use a relativistic ionization front to provide various initial transverse wakefield amplitudes for the self-modulation of a long proton bunch in plasma. We show experimentally that, with sufficient initial amplitude [≥(4.1±0.4) MV/m], the phase of the modulation along the bunch is reproducible from event to event, with 3%-7% (of 2π) rms variations all along the bunch. The phase is not reproducible for lower initial amplitudes. We observe the transition between these two regimes. Phase reproducibility is essential for deterministic external injection of particles to be accelerated.

The effect of the laser pulse shape on the wakefield generation in field-ionized plasma

In this paper, the effect of the laser pulse shape on the generation and evolution of the wakefield during the interaction of the intense laser pulse with the gas have been studied utilizing the parallel relativistic PIC simulation code. In order to reach this aim, three pulses with length 300 fs and different rise-times 30, 45, and 60 are typically selected. Our results show that, the amplitude of the laser wakefield produced in the gas in comparison with the plasma strongly depends on the laser pulse shape. The simulation results indicate that for the high-slope laser pulse time (here 30 fs), ionization and thus density fluctuations have no significant effect on the wakefield generation because of rapid increase of the laser electric field. While by increasing the laser pulse rise-time to 45 fs, the rapid wave breaking due to the change in the medium refractive index during the gas ionization, prevents from the wakefield amplitude growth, so that the wakefield with larger amplitude is emerged in the plasma. For a slow-sloping pulse (here 60 fs), the ratio of the wakefield generation in the gas to the plasma is altered for the different gas densities and laser intensities. Moreover, it is represented that the longer the laser pulse rise-time, the sooner difference between the wakefield produced in the gas and plasma is observed. In fact, the larger the rise-time, the greater the density fluctuations and, consequently, the larger the initial noise is generated to seed the Raman instability.

Experimental study of extended timescale dynamics of a plasma wakefield driven by a self-modulated proton bunch

Plasma wakefield dynamics over timescales up to 800 ps, approximately 100 plasma periods, are studied experimentally at the Advanced Wakefield Experiment (AWAKE). The development of the longitudinal wakefield amplitude driven by a self-modulated proton bunch is measured using the external injection of witness electrons that sample the fields. In simulation, resonant excitation of the wakefield causes plasma electron trajectory crossing, resulting in the development of a potential outside the plasma boundary as electrons are transversely ejected. Trends consistent with the presence of this potential are experimentally measured and their dependence on wakefield amplitude are studied via seed laser timing scans and electron injection delay scans.

Experimental measurement of the wake field in a plasma filament created by a single-color ultrafast laser pulse

A laser plasma wake field in a single-color femtosecond laser filament determines the acceleration of ionized electrons, which affects the intensity and bandwidth of the emitted terahertz wave and is important for understanding the fundamental nonlinear process of THz generation. Since the THz wave generated by a laser wake field is extremely small and easily hidden by other THz generation mechanisms, no method exists to measure this wake field directly. In this paper, a simple and stable method for determining the amplitude of the laser plasma wake field is presented. Based on the cancellation of a positive laser plasma wake field and an external negative electric field, the "zero point" of the intensity of the generated THz wave at some frequency can be used to determine the exact amplitude of the corresponding laser plasma wake field. This finding opens an avenue toward the clarification of ultrafast electronic dynamic processes in laser-induced plasmas.

Modulation of the Amplitude and Spatial Structure of the Plasma Wakefield With Super-Gaussian Chirped Laser Pulse

The effects of super-Gaussian chirped laser pulse and inhomogeneity of plasma on space distribution and amplitude of wakefield are studied. The different super-Gaussian chirped laser pulse envelopes are used to strike the uniform and various inhomogeneous plasmas. The results show that compared with the unchirped laser pulse, the chirped laser pulse can enhance the wakefield generation, make the bubbles’ structure deformative seriously, reduce the numbers of bubbles in the same longitudinal distance, and enlarge the size of the wakefield bubbles. Besides, the stronger wakefield is generated in inhomogeneous plasma compared with a uniform one. Moreover, the characteristics of the wakefield can be controlled efficiently by the super-Gaussian pulse index. That is, the amplitude and spatial structure of the plasma wakefield can be modulated by the super-Gaussian chirped laser pulse and the inhomogeneity of the plasma.