Relativistic Electron Beam Transport Research Articles

Verification and benchmarking relativistic electron beam transport through a background gas

It is necessary to establish confidence in high-consequence codes containing an extensive suite of physics algorithms in the regimes of interest. Verification problems allow code developers to assess numerical accuracy and increase confidence that specific sets of model physics were implemented correctly in the code. The two main verification techniques are code verification and solution verification. In this work, we present verification problems that can be used in other codes to increase confidence in simulations of relativistic beam transport. Specifically, we use the general plasma code EMPIRE to model and compare with the analytical solution to the evolution of the outer radial envelope of a relativistic charged particle beam. We also outline a benchmark test of a relativistic beam propagating through a vacuum and pressurized gas cell, and present the results between EMPIRE and the hybrid code GAZEL. Further, we discuss the subtle errors that were caught with these problems and detail lessons learned.

Dependence of resistivity gradient guiding of laser-driven relativistic electron beams on laser intensity and duration

A laser-driven relativistic electron beam (REB) has a large beam divergence. For the efficient heating of material by REB, for example, core heating in fast ignition, beam guiding from its generation point to the heating material to be heated by suppressing spatial divergence in a perpendicular direction to keep its intensity sufficiently high is indispensable. We evaluated the dependences of the REB guiding performance in the resistivity gradient guiding scheme [A. P. L. Robinson and M. Sherlock, “Magnetic collimation of fast electrons produced by ultraintense laser irradiation by structuring the target composition,” Phys. Plasmas 14, 083105 (2007)] on laser intensity and duration, from the present petawatt laser parameters to the fast ignition-relevant laser parameters, in terms of the temperature dependence of resistivity and energy deposition of the REB. The REB transport simulations in solid materials show that for a fast ignition-relevant laser condition, a nickel cylinder works as a guiding material; an REB transport efficiency of 40% is obtained for a 100-μm propagation. The simulation results show that the resistive gradient guiding scheme is one of possible candidates for improving core heating efficiency.

Simulation study of coupled two-stream and current filamentation instability excited by accelerator electron beams in plasmas

A gas-discharge plasma device is simulated with COMSOL software, and the obtained plasma density profile is input into a two-dimensional particle-in-cell code, in which the transport of relativistic electron beams in the plasma with an actual density profile is investigated. The results show that the device can produce a wide range of high-density plasmas with the maximum density approaching 5.25×1022 m−3. With the relativistic electron beams produced from a linear electron accelerator, the gas-discharge plasma is shown to be an ideal medium for the investigation of coupled two-stream and current filamentation instability.

Stable transport of relativistic electron beams in plasmas

The long-distance stable transport of relativistic electron beams (REBs) in plasmas is studied by full three-dimensional particle-in-cell simulations. Theoretical analysis shows that the beam transport is mainly influenced by three transverse instabilities, where the excitation of self-modulation instability, and the suppression of the filamentation instability and the hosing instability are important to realize the beam stable transport. By modulating the transport parameters such as the electron density ratio, the relativistic Lorentz factor, the beam envelopes and the density profiles, the relativistic bunches having a smooth density profile and a length of several plasma wave periods can suppress the beam-plasma instabilities and propagate in plasmas for long distances with small energy losses. The results provide a reference for the research of long-distance and stable transport of REBs, and would be helpful for new particle beam diagnosis technology and space active experiments.

Nanoscale Electrostatic Modulation of Mega-Ampere Electron Current in Solid-Density Plasmas.

Transport of high-current relativistic electron beams in dense plasmas is of interest in many areas of research. However, so far the mechanism of such beam-plasma interaction is still not well understood due to the appearance of small time- and space-scale effects. Here we identify a new regime of electron beam transport in solid-density plasma, where kinetic effects that develop on small time and space scales play a dominant role. Our three-dimensional particle-in-cell simulations show that in this regime the electron beam can evolve into layered short microelectron bunches when collisions are relatively weak. The phenomenon is attributed to a secondary instability, on the space- and timescales of the electron skin depth (tens of nanometers) and few femtoseconds of strong electrostatic modulation of the microelectron current filaments formed by Weibel-like instability of the original electron beam. Analytical analysis on the amplitude, scale length, and excitation condition of the self-generated electrostatic fields is clearly validated by the simulations.

Electron beam propagation and magnetic structure formation in a strongly magnetized, collisional plasma

Collisional effects on relativistic electron beam transport through high-density magnetized plasma are studied numerically and theoretically. An electron beam injected into cold high-density plasma induces the Weibel instability generating magnetic field components transverse to the direction of beam propagation. This field scatters the beam electrons. While an applied magnetic field suppresses the instability, collisions in the background plasma enhance the instability. This interesting result is verified by a dispersion relation derived based on a set of two fluid equations. We give a physical interpretation using a simple theoretical model. We also analyze the nonlinear evolution of the collisional magnetized beam-plasma interaction using a hybrid simulation code. As a result, it is found that a large scale structure is produced in the collisional plasma by an enhanced induced longitudinal electric field.

Enhanced collective stopping and drift of electron beams in fusion plasmas with heavy-ion species

The transport and energy deposition of relativistic electron beams in transversely nonuniform plasmas are investigated with two-dimensional electromagnetic particle-in-cell simulations. For the beam with radius much larger than plasma skin depth, the current filamentation instability excited by the electron beam can be observed, which breaks the beam into filaments and leads to the formation of strong magnetic fields consequently. The effects of plasma ion species are significant and asymmetric transverse magnetic fields are formed in plasmas with heavy-ion species due to the asymmetric neutralization of beam space charge by plasma ions. The asymmetric transverse magnetic fields contribute to the directional drift of beam electrons to lower plasma density regions, which may accelerate the filaments merger process and lead to highly localized beam-energy deposition in plasmas.

Transport of kJ-laser-driven relativistic electron beams in cold and shock-heated vitreous carbon and diamond

We report experimental results on relativistic electron beam (REB) transport in a set of cold and shock-heated carbon samples using the high-intensity kilojoule-class OMEGA EP laser. The REB energy distribution and transport were diagnosed using an electron spectrometer and x-ray fluorescence measurements from a Cu tracer buried at the rear side of the samples. The measured rear REB density shows brighter and narrower signals when the targets were shock-heated. Hybrid PIC simulations using advanced resistivity models in the target warm-dense-matter (WDM) conditions confirm this observation. We show that the resistivity response of the media, which governs the self-generated resistive fields, is of paramount importance to understand and correctly predict the REB transport.

Longitudinal magnetic field generation during the early stage of relativistic electron beam-plasma interaction

A mechanism for longitudinal magnetic field (i.e., the magnetic field parallel to the beam propagation direction) generation during the transport of relativistic electron beams with large edge gradients, through a high density plasma, is explained using two-dimensional (2D) particle-in-cell simulations and analytical theory. A ring structure is first formed due to the unneutralized beam current in the edge. Later, the counter-propagation of plasma return currents in the radial direction is excited due to the induction of a defocusing azimuthal magnetic field in the inner parts of the ring structure, with a characteristic crossing length of the ring width. Finally, the filamentation of plasma radial return currents in the azimuthal direction develops and contributes to the generation of a strong longitudinal magnetic field, which is shown to have strength on the same order of the transverse magnetic fields.

Effect of target material on relativistic electron beam transport

A computational study using the hybrid-particle-in-cell code ZUMA investigated the transport of a fast electron beam (55 J, 1013 A/cm2) produced at Titan laser conditions (λ = 1 μm, 0.7 ps, 1020 W/cm2) in materials ranging from the low to high atomic number, specifically fast electron stopping and the evolution of resistive magnetic fields. Fast electron energy loss due to stopping was similar in Al, Cu, and Ag (21%–27%) and much higher in Au (54%). Ohmic stopping was found to dominate over collisional stopping in all materials except Au. Resistive magnetic field growth was shown to depend on the dynamic competition between the resistivity and resistivity gradient source terms in Faraday's Law. Moreover, the dependence of these terms on the background material ionization state and temperature evolution is presented. The advantages of mid-Z materials for collimation are discussed, as well as the implications for collimation at fast ignition conditions.

Modulation of proton beams by relativistic electron beam-plasma instability

Two-dimensional electromagnetic particle-in-cell simulations are performed to investigate the transport of relativistic electron beams co-moved with a proton beam in background plasmas. For the beam with the radius much larger than the plasma skin depth, the current filamentation instability excited by the relativistic electron beam can be clearly observed and the transverse magnetic fields in the plasma increase significantly. The proton beam is modulated strongly by the electromagnetic fields in plasmas, and a netlike structure in the beam profile is formed with a high density contrast, which can be provided as an effective tool to diagnose the instability. The dynamic effects of plasma ions are shown to be important and play a significant role in the dynamic evolution of the proton beam.

Formation and Transport of a Dense Electron Beam with Near-Rectangular Cross Section

Problems of formation and transport of relativistic electron beams with straight axis and near-rectangular cross section keeping its initial orientation in the process of evolution are considered.

Stagnation of electron flow by a nonlinearly generated whistler wave

Relativistic electron beam transport through a high-density, magnetized plasma is studied numerically and theoretically. An electron beam injected into a cold plasma excites Weibel and two-stream instabilities that heat the beam and saturate. In the absence of an applied magnetic field, the heated beam continues to propagate. However, when a magnetic field of particular strength is applied along the direction of beam propagation, a secondary instability of off-angle whistler modes is excited. These modes then couple nonlinearly creating a large amplitude parallel-propagating whistler that stops the beam. Here, we will show these phenomena in detail and explain the mechanism of whistler mediated beam stagnation.

Fast ignition realization experiment with high-contrast kilo-joule peta-watt LFEX laser and strong external magnetic field

A petawatt laser for fast ignition experiments (LFEX) laser system [N. Miyanaga et al., J. Phys. IV France 133, 81 (2006)], which is currently capable of delivering 2 kJ in a 1.5 ps pulse using 4 laser beams, has been constructed beside the GEKKO-XII laser facility for demonstrating efficient fast heating of a dense plasma up to the ignition temperature under the auspices of the Fast Ignition Realization EXperiment (FIREX) project [H. Azechi et al., Nucl. Fusion 49, 104024 (2009)]. In the FIREX experiment, a cone is attached to a spherical target containing a fuel to prevent a corona plasma from entering the path of the intense heating LFEX laser beams. The LFEX laser beams are focused at the tip of the cone to generate a relativistic electron beam (REB), which heats a dense fuel core generated by compression of a spherical deuterized plastic target induced by the GEKKO-XII laser beams. Recent studies indicate that the current heating efficiency is only 0.4%, and three requirements to achieve higher efficiency of the fast ignition (FI) scheme with the current GEKKO and LFEX systems have been identified: (i) reduction of the high energy tail of the REB; (ii) formation of a fuel core with high areal density using a limited number (twelve) of GEKKO-XII laser beams as well as a limited energy (4 kJ of 0.53-μm light in a 1.3 ns pulse); (iii) guiding and focusing of the REB to the fuel core. Laser–plasma interactions in a long-scale plasma generate electrons that are too energetic to efficiently heat the fuel core. Three actions were taken to meet the first requirement. First, the intensity contrast of the foot pulses to the main pulses of the LFEX was improved to >109. Second, a 5.5-mm-long cone was introduced to reduce pre-heating of the inner cone wall caused by illumination of the unconverted 1.053-μm light of implosion beam (GEKKO-XII). Third, the outside of the cone wall was coated with a 40-μm plastic layer to protect it from the pressure caused by imploding plasma. Following the above improvements, conversion of 13% of the LFEX laser energy to a low energy portion of the REB, whose slope temperature is 0.7 MeV, which is close to the ponderomotive scaling value, was achieved. To meet the second requirement, the compression of a solid spherical ball with a diameter of 200-μm to form a dense core with an areal density of ∼0.07 g/cm2 was induced by a laser-driven spherically converging shock wave. Converging shock compression is more hydrodynamically stable compared to shell implosion, while a hot spot cannot be generated with a solid ball target. Solid ball compression is preferable also for compressing an external magnetic field to collimate the REB to the fuel core, due to the relatively small magnetic Reynolds number of the shock compressed region. To meet the third requirement, we have generated a strong kilo-tesla magnetic field using a laser-driven capacitor-coil target. The strength and time history of the magnetic field were characterized with proton deflectometry and a B-dot probe. Guidance of the REB using a 0.6-kT field in a planar geometry has been demonstrated at the LULI 2000 laser facility. In a realistic FI scenario, a magnetic mirror is formed between the REB generation point and the fuel core. The effects of the strong magnetic field on not only REB transport but also plasma compression were studied using numerical simulations. According to the transport calculations, the heating efficiency can be improved from 0.4% to 4% by the GEKKO and LFEX laser system by meeting the three requirements described above. This efficiency is scalable to 10% of the heating efficiency by increasing the areal density of the fuel core.

Heating efficiency evaluation with mimicking plasma conditions of integrated fast-ignition experiment.

A series of experiments were carried out to evaluate the energy-coupling efficiency from heating laser to a fuel core in the fast-ignition scheme of laser-driven inertial confinement fusion. Although the efficiency is determined by a wide variety of complex physics, from intense laser plasma interactions to the properties of high-energy density plasmas and the transport of relativistic electron beams (REB), here we simplify the physics by breaking down the efficiency into three measurable parameters: (i) energy conversion ratio from laser to REB, (ii) probability of collision between the REB and the fusion fuel core, and (iii) fraction of energy deposited in the fuel core from the REB. These three parameters were measured with the newly developed experimental platform designed for mimicking the plasma conditions of a realistic integrated fast-ignition experiment. The experimental results indicate that the high-energy tail of REB must be suppressed to heat the fuel core efficiently.

Physical studies of fast ignition in China

Fast ignition approach to inertial confinement fusion is one of the important goals today, in addition to central hot spot ignition in China. The SG-IIU and PW laser facilities are coupled to investigate the hot spot formation for fast ignition. The SG-III laser facility is almost completed and will be coupled with tens kJ PW lasers for the demonstration of fast ignition. In recent years, for physical studies of fast ignition, we have been focusing on the experimental study of implosion symmetry, M-band radiation preheating and mixing, advanced fast ignition target design, and so on. In addition, the modeling capabilities and code developments enhanced our ability to perform the hydro-simulation of the compression implosion, and the particle-in-cell (PIC) and hybrid-PIC simulation of the generation, transport and deposition of relativistic electron beams. Considerable progress has been achieved in understanding the critical issues of fast ignition.

A reduced model for relativistic electron beam transport in solids and dense plasmas

A hybrid reduced model for relativistic electron beam transport based on the angular moments of the relativistic kinetic equation with a special closure is presented. It takes into account collective effects with the self-generated electromagnetic fields as well as collisional effects with the slowing down of the relativistic electrons by plasmons, bound and free electrons and their angular scattering on both ions and electrons. This model allows for fast computations of relativistic electron beam transport while describing their energy distribution evolution. Despite the loss of information concerning the angular distribution of the electron beam, the model reproduces analytical estimates in the academic case of a monodirectional and monoenergetic electron beam propagating through a warm and dense plasma and hybrid particle-in-cell simulation results in a realistic laser-generated electron beam transport case.

Unraveling resistive versus collisional contributions to relativistic electron beam stopping power in cold-solid and in warm-dense plasmas

We present results on laser-driven relativistic electron beam propagation through aluminum samples, which are either solid and cold or compressed and heated by laser-induced shock. A full numerical description of fast electron generation and transport is found to reproduce the experimental absolute Kα yield and spot size measurements for varying target thicknesses, and to sequentially quantify the collisional and resistive electron stopping powers. The results demonstrate that both stopping mechanisms are enhanced in compressed Al samples and are attributed to the increase in the medium density and resistivity, respectively. For the achieved time- and space-averaged electronic current density, ⟨jh⟩∼8×1010 A/cm2 in the samples, the collisional and resistive stopping powers in warm and compressed Al are estimated to be 1.5 keV/μm and 0.8 keV/μm, respectively. By contrast, for cold and solid Al, the corresponding estimated values are 1.1 keV/μm and 0.6 keV/μm. Prospective numerical simulations involving higher jh show that the resistive stopping power can reach the same level as the collisional one. In addition to the effects of compression, the effect of the transient behavior of the resistivity of Al during relativistic electron beam transport becomes progressively more dominant, and for a significantly high current density, jh∼1012 A/cm2, cancels the difference in the electron resistive stopping power (or the total stopping power in units of areal density) between solid and compressed samples. Analytical calculations extend the analysis up to jh=1014 A/cm2 (representative of the full-scale fast ignition scenario of inertial confinement fusion), where a very rapid transition to the Spitzer resistivity regime saturates the resistive stopping power, averaged over the electron beam duration, to values of ∼1 keV/μm.

Effects of the imposed magnetic field on the production and transport of relativistic electron beams

The effects of the imposed uniform magnetic field, ranging from 1 MG up to 50 MG, on the production and transport of relativistic electron beams (REBs) in overdense plasmas irradiated by ultraintense laser pulse are investigated with two-dimensional particle-in-cell numerical simulations. This study gives clear evidence that the imposed magnetic field is capable of effectively confining the relativistic electrons in space even when the source is highly divergent since it forces the electrons moving helically. In comparison, the spontaneous magnetic fields, generated by the helically moving electrons interplaying with the current filamentation instability, are dominant in scattering the relativistic electrons. As the imposed magnetic field was increased from 1 MG to 50 MG, overall coupling from laser to the relativistic electrons which have the potential to heat the compressed core in fast ignition was found to increase from 6.9% to 21.3% while the divergence of the REB increases significantly from 64° to 90°. The simulations show that imposed magnetic field of the value of 3–30 MG could be more suitable to fast-ignition inertial fusion.

Vlasov-Fokker-Planck simulations of fast-electron transport with hydrodynamic plasma response

We report on kinetic simulations of the transport of laser-produced relativistic electron beams (REB) through solid-density plasma, including the hydrodynamic response of the plasma. We consider REBs with parameters relevant to fast-ignition of compressed inertial confinement fusion capsules. We show that over the 10–20ps timescales required for fast-ignition, thermal pressure (from Ohmic heating) can significantly modify the density which in turn strongly affects the propagation of injected fast-electrons; it allows them to re-collimate into a narrow, intense beam under conditions where they initially undergo beam-hollowing. Similar static-density calculations do not show re-collimation. The re-collimation effect is attributed to PdV cooling in the pressure-induced density-channel, which in turn suppresses defocusing magnetic fields generated by resistivity gradients. These simulations have been carried out using the new 2D-3V Vlasov-Fokker-Planck (VFP) code FIDO running in hybrid mode.