Plasma Return Current Research Articles

Enhanced energy deposition of laser-produced proton beams in high-density plasmas due to beam density self-steepening

The energy deposition of laser-accelerated proton beams in solid-density plasmas with different ion charge numbers is studied with detailed one-dimensional particle-in-cell simulations. In the plasma with a high ion charge number, in which the plasma collision frequency approaches electron oscillation frequency, the beam protons are strongly decelerated by the electric field induced by the plasma return current. The energy deposition is further enhanced as the beam travel distance increases due to beam density self-steeping, which is also confirmed by multi-dimensional particle-in-cell simulation. A simple analytical model is proposed to estimate the characteristic travel distance for significant density self-steeping, showing agreement with the simulation results. While in the plasma with a low ion charge number, in which the plasma collision frequency is much smaller than the electron oscillation frequency, the proton beam is modulated significantly by the excited two-stream instability.

Magnetic pinching of relativistic particle beams: a new approach to strong-field QED physics

Quantum electrodynamics (QED) is a foundation of modern physics, yet access to the strong-field QED regime in the laboratory remains a formidable challenge. Currently, high-power lasers at the multi-petawatt level and above are generally believed to be an important approach to test QED physics. Here, we present a different approach by use of an electron beam self-pinched to near-solid-density. The beam self-pinching is realized while it transports through a properly designed hollow cone target, where strong azimuthal magnetic fields are generated by the beam-induced plasma return currents at the inner surface of the cone target. In this way, the beam diameter can be reduced by more than an order of magnitude down to submicron and its density is increased by hundreds of times. The produced ultradense electron beams can unlock a new regime of QED-dominated beam–plasma interactions, for example, more than 60% of the beam energy can be converted into GeV gamma-rays with unprecedented brilliance when such a beam passes through a thin solid foil. Moreover, with proper parameter design, this beam-focusing scheme can also be applied to positron beams and thus may find applications in broad areas, such as particle colliders and strong-field physics.

Hybrid modelling of cavity system generated electromagnetic pulse in low pressure air

The surface of metal system exposed to ionizing radiation (X-ray and γ-ray) will emit high-energy electrons through the photoelectric effect and other processes. The transient electromagnetic field generated by the high-speed electron flow is called system generated electromagnetic pulse (SGEMP), which is difficult to shield effectively. An ongoing effort has been made to investigate the SGEMP response in vacuum by numerical simulation. However, the systems are usually operated in a gaseous environment. The objective of this paper is to investigate the effect of low-pressure air on the SGEMP. A three-dimensional hybrid simulation model is developed to calculate the characteristics of the electron beam induced air plasma and its interaction with the electromagnetic field. In the hybrid model, the high-energy photoelectrons are modelled as macroparticles, and secondary electrons are treaed as fluid for a balance between efficiency and accuracy. A cylindrical cavity with an inner diameter of 100 mm and a length of 50 mm is used. The photoelectrons are emitted from one end of the cavity and are assumed to be monoenergetic (20 keV). The photoelectron pulse follows a sine-squared distribution with a peak current density of 10 A/cm<sup>2</sup>, and its full width at half maximum is 2 ns. The results show that the number density of the secondary electrons near the photoelectron emission surface and its axial gradient increase as air pressure increases. The electron number density in the middle of the cavity shows a peak value at 20 Torr (1 Torr = 133 Pa). The electron temperature decreases monotonically with the increase in pressure. The low-pressure air plasma in the cavity prevents the space charge layer from being generated. The peak value of the electric field is an order of magnitude lower than that in vacuum, and the pulse width is also significantly reduced. The emission characteristic of the photoelectrons determines the peak value of the current response. The current reaching the end of the cavity surface first increases and then decreases with pressure increasing. The plasma return current can suppress the rising rate of the total current and extend the duration of current responses. Finally, to validate the established hybrid simulation model, the calculated magnetic field is compared with that from the benchmark experiments. This paper helps to achieve a better prediction of the SGEMP response in a gaseous environment. Compared with the particle-in-cell Monte Carlo collision method, the hybrid model adopted can greatly reduce the computational cost.

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.

Space Weather Influence on Relative Motion Control using the Touchless Electrostatic Tractor

With recent interest in the use of electrostatic forces for contactless tugging and attitude control of noncooperative objects for orbital servicing and active debris mitigation, the need for a method of remote charge control arises. In this paper, the use of a directed electron beam for remote charge control is considered in conjunction with the relative motion control. A tug vehicle emits an electron beam onto a deputy object, charging it negatively. At the same time, the tug is charged positively due to beam emission, resulting in an attractive electrostatic force. The relative position feedback control between the tug and the passive debris object is studied subject to the charging being created through an electron beam. Employing the nominal variations of the GEO space weather conditions across longitude slots, two electrostatic tugging strategies are considered. First, the electron beam current is adjusted throughout the orbit in order to maximize this resulting electrostatic force. This open-loop control strategy compensates for changes in the nominally expected local space weather environment in the GEO region to adjust for fluctuations in the local plasma return currents. Second, the performance impact of using a fixed electron beam current on the electrostatic tractor is studied if the same natural space weather variations are assumed. The fixed electron beam current shows a minor performance penalty (<5 %) while providing a much simpler implementation that does not require any knowledge of local space weather conditions.

Self-pinched ion beam transport in plasmas with finite radius and nonuniform transverse density

The self-pinched ion beam transport in plasmas with finite radius and nonuniform transverse density profile are investigated with a two-dimensional electromagnetic particle-in-cell simulation code. Electron holes are formed in such plasmas due to the attraction of the ion beam and are shown to propagate with the ion beam. The ion beam charge can be overcompensated by the plasma electrons provided that the radial density distribution of the ion beam overlaps with the electron holes. In this case, the radial electric field exerted on the beam ions increases significantly and becomes focusing. The plasma return current is found to enhance the ion beam current, leading to a higher self-pinched force in the radial direction. An ion beam with higher density and small radius thus can be obtained in such plasmas, which is favorite for the self-pinched ion beam transport.

ELECTRON HEATING, MAGNETIC FIELD AMPLIFICATION, AND COSMIC-RAY PRECURSOR LENGTH AT SUPERNOVA REMNANT SHOCKS

We investigate the observability, by direct and indirect means, of a shock precursor arising from magnetic field amplification by cosmic rays. We estimate the depth of such a precursor under conditions of nonresonant amplification, which can provide magnetic field strengths comparable to those inferred for supernova remnants. Magnetic field generation occurs as the streaming cosmic rays induce a plasma return current, and may be quenched either by nonresonant or resonant channels. In the case of nonresonant saturation, the cosmic rays become magnetized and amplification saturates at higher magnetic fields. The precursor can extend out to $10^{17} - 10^{18}$ cm and is potentially detectable. If resonant saturation occurs, the cosmic rays are scattered by turbulence and the precursor length will likely be much smaller. The dependence of precursor length on shock velocity has implications for electron heating. In the case of resonant saturation, this dependence is similar to that in the more familiar resonantly generated shock precursor, which when expressed in terms of the cosmic ray diffusion coefficient $\varkappa $ and shock velocity $v_s$ is $\varkappa /v_s$. In the nonresonantly saturated case, the precursor length declines less quickly with increasing $v_s$. Where precursor length proportional to $1/v_s$ gives constant electron heating, this increased precursor length could be expected to lead to higher electron temperatures for nonresonant amplification. This should be expected at faster supernova remnant shocks than studied by previous works. Existing results and new data analysis of SN 1006 and Cas A suggest some observational support for this idea.

Effect of beam current on dispersion relation of plasma-filled dielectric Cherenkov maser

Using plasma fluid theory, from linear perturbation equations, the effect of the beam current size on the dispersion relation of plasma-filled dielectric Cherenkov maser is examined when the beam current is complete, or not effectively neutralized by the return current in the background plasma. The dispersion relation and the wave growth of the TM0n are solved under both cases. Based on this, a discussion on the effect of the beam current on the dispersion relation and wave growth is given. Both of the cases of plasma return current can or not effectively neutralized electron beams current has different dispersion relation and wave growth. When the parameters of waveguide and plasma are fixed, the electron beam current is not the bigger the better, too large electron beam current is harmful for improving the efficiency of the device, and there has an optimal matching relationship between them.

Back-reaction instabilities of relativistic cosmic rays

We explore streaming instabilities of an electron–ion plasma with relativistic and ultra-relativistic cosmic rays in the background magnetic field using the multi-fluid approach. Cosmic rays can be both electrons and ions. The drift speed of cosmic rays is directed along the magnetic field. In equilibrium, the return current of the background plasma is taken into account. One-dimensional perturbations parallel to the magnetic field are considered. The dispersion relations are derived for transverse and longitudinal perturbations. It is shown that the back-reaction of magnetized cosmic rays generates new instabilities one of which has a growth rate that can approach the growth rate of the Bell instability. These new instabilities can be stronger than the cyclotron resonance instability. For unmagnetized cosmic rays, the growth rate is analogous to the Bell one. We compare two models of the plasma return current in equilibrium with three and four charged components. Some differences between these models are demonstrated. For longitudinal perturbations, an instability is found in the case of ultra-relativistic cosmic rays. The results obtained can be applied to investigation of astrophysical objects such as the shocks by supernova remnants, galaxy clusters, intracluster medium and so on, where interaction of cosmic rays with turbulence of the electron–ion plasma produced by them is of great importance for cosmic-ray evolution.

Analytic model of electron beam thermalization during the resistive Weibel instability

A novel theoretical model for underdense electron beam propagation during the nonlinear stage of the resistive Weibel instability (WI) is presented and is used to calculate the stopping time of the beam. The model and supporting simulation results lead to the conclusion that the WI initially enhances beam deceleration but then reduces it when compared to a filamentation-suppressed beam (without WI), so that the overall stopping time of the beam is essentially unaffected by the instability. Using the theoretical model, a criterion is derived that determines when deceleration is no longer enhanced by the instability. We also demonstrate that exotic plasma return current distributions can be obtained within and outside of beam filaments that sharply contrast those observed in collisionless systems. For example, the plasma return current is reversed in selected areas.

Stability properties of the electron return current for intense ion beam propagation through background plasma

AbstractWhen an intense ion beam propagates through a dense background plasma, its current is partially neutralized by the electron plasma return current. Due to the non-uniformity of the background plasma electrons longitudinal velocity profile ${\bar v}$(r), the flow can be unstable. The instability is similar to the Kelvin-Helmholz instability for the non-uniform flow of an incompressible neutral fluid, with the electrostatic potential playing the role of pressure. For the case of electron return current flow, the significant new feature is the presence of the partially self-neutralized magnetic field of the ion beam, which significantly affects the evolution of small-amplitude excitations. In this paper the stability properties of the flow of electrons making up the plasma return current is investigated using the macroscopic cold-fluid-Maxwell equations. It is shown that this flow may become unstable, but the instability growth rates are exponentially small. This unstable body mode is qualitatively different from previously studied surface-mode excitations of the electron plasma return current for an intense ion beam with a sharp radial boundary, which is found to be stable due to the stabilizing influence of the partially neutralized magnetic field of the ion beam.

Collective electric field effects on the confinement of fast ions in tokamaks

The injection of neutral particle beams counter to the plasma current direction in the Mega-Ampère Spherical Tokamak (MAST) [A. Sykes, R. J. Akers, L. C. Appel et al., Nucl. Fusion, 41, 1423 (2001)] leads to substantial losses of energetic beam ions and also rapid toroidal rotation. The electrodynamic consequences of energetic ion loss on tokamak plasmas are explored in light of results from the MAST counterinjection experiments and test particle calculations of the current density due to escaping ions. Previous authors have noted that there are two possible consequences of such a current: either a compensating bulk plasma return current is set up, or the plasma behaves as an insulator, with the energetic ion current balanced by a displacement current rather than a conduction current. Radial electric fields and hence toroidal flows occur in both cases, but higher fields are predicted in the insulating case. Such fields are important because they can confine both fast ions and bulk plasma (via the suppression of turbulent transport). The return current scenario, which appears to be operative during counterinjection in MAST, is shown to be applicable if there is a sufficiently high level of momentum transport in the bulk ions; electrons cannot carry the return current, although they contribute to an ambipolar particle flux on the plasma confinement time scale. The insulating scenario may be applicable to high confinement regimes in burning tokamak plasmas.

Electromagnetic instabilities for relativistic beam-plasma interaction in wholekspace: Nonrelativistic beam and plasma temperature effects

For the system formed by a relativistic electron beam and its plasma return current, we investigate the effects of both transverse and parallel beam and plasma temperatures on the linear stability of collective electromagnetic modes. We focus on nonrelativistic temperatures and wave-vector orientations ranging from two-stream to filamentation instabilities. Water-bag distributions are used to model temperature effects and we discuss their relevance. Labeling Theta(k) the angle between the beam and the wave vector, one or two critical angles Theta(c,i) are determined exactly and separate the k space into two parts. Modes with Theta(k) < Theta(c) =min ( Theta(c,i)) are quasilongitudinal and poorly affected by any kind of temperature. Modes having Theta(k) > Theta(c) are very sensitive to transverse beam and plasma parallel temperatures. Also, parallel plasma temperature can trigger a transition between the beam-dependent filamentation instability (Theta(k) =pi/2) and the plasma-temperature-dependent Weibel instability so that two-stream, filamentation, and Weibel instabilities are eventually closely connected to each other. The maximum growth rate being reached for a mode with Theta(k) < Theta(c), no temperature of any kind can significantly reduce it in the nonrelativistic temperature regime.

Photoemission current‐spacecraft voltage relation: Key to routine, quantitative low‐energy plasma measurements

Measurements of the floating potential and plasma return current on the GGS‐Polar spacecraft are used to determine the equilibrium photoemission current, Jħv, as a function of the spacecraft's (S/C) “floating potential,” ΔΦS/C. The photoemission current function is found to be time independent using nearly 10 months of GGS‐Polar data from April 1996 to March 1997 including 1.6 million separate spectra from the Hydra (hot plasma) and EFI (electric field) instruments. The photoemission current density leaving the spacecraft at positive floating potentials ΔΦS/C &lt; 50 V is well fit by a sum of two exponentials of the form: Jħv(μA/m2) = A exp ( −ΔΦS/C/B) + C exp (−ΔΦS/C/D), where best fit estimates A ≃ 152 ± 57 μA/m2, B ≃ 1.7 ± 0.2 eV, C ≃ 0.86 ± 0.29 μA/m2, and D ≃ 9.5 ± 1.0 eV. In equilibrium this photoemission current density is determined from the ratio of sunlit to spacecraft areas and the plasma current density, JRC, collected by the spacecraft. For the Polar spacecraft this ratio of areas is not constant in time, and the observed return current voltage relation is time dependent. After correction for the orbitally induced time‐dependent ratio of areas, the photoemission curve reported above is obtained and is essentially time independent. After correcting for the different procedures used the present results are illustrated to be consistent with early results with less resolution reported by Pedersen [1995]. When the sensing of the floating potential by EFI on the spacecraft is interrupted, the photoemission‐voltage relationship is essential for the assignment of the ambient kinetic energy of the detected particle fluxes. We demonstrate a method using the plasma data and the statistical return current relationship that recovers the floating potential of the spacecraft with a typical precision that is the larger of 0.5 V and 0.1ΔΦS/C We also demonstrate that the ion and electron densities determined by numerical integration over distributions corrected with opposite energy shifts implied by the potential enhances their routine agreement, a further check on the absolute precision of the potential inferences. The “systematic” departures of 40% of the data from the statistically defined Jħv(ΔΦS/C) curve reported above are time varying and organized in radius and with L shell. These data are inferred to be the signature of missing ambient plasma currents to the spacecraft that are not directly detected by the Hydra instrumentation (cf. X. Cao et al., Properties of very cold (Te ≃ 0.1 eV) electrons within the magnetosphere, submitted to Journal of Geophysical Research, 1999).

Observation of Return Current Effects in a Passive Plasma Lens

Observations of relativistic beam focusing by a passive plasma lens have demonstrated a reduction in focusing strength due to plasma return current. A 50 MeV beam was propagated through a 1--3 cm long plasma with density around ${10}^{14}{\mathrm{cm}}^{\ensuremath{-}3}$. Beam size was measured as a function of propagation distance. For a ratio of collisionless plasma skin depth to beam spot size ${k}_{p}{\ensuremath{\sigma}}_{r}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.33$, no significant reduction in focusing was observed. Reduced focusing was measured for ${k}_{p}{\ensuremath{\sigma}}_{r}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.1$, where a significant fraction of the inductively driven return current in the plasma flows within the beam. The observations are in good agreement with an envelope equation model and with particle-in-cell simulations.

Resistive hose instability for arbitrary skin depth

Resistive hose growth for moderate or large skin depth differs from that derived from a conductivity model. Asymptotic growth is calculated for the Bennett equilibrium, incorporating the inductive component in the plasma return current, with phase mixing accounted for via the `distributed-mass' model. Analytic scalings are checked with numerical solutions of the linearized model. For a ratio of skin depth to beam radius of less than 1/10 the conductivity model appears quite adequate. When this ratio exceeds 1/4 inductive corrections appear.

Current neutralization and focusing of intense ion beams with a plasma-filled solenoidal lens. I

The response of the magnetized plasma in an axisymmetric, plasma-filled, solenoidal magnetic lens, to intense light ion beam injection is studied. The lens plasma fill is modeled as an inertialess, resistive, electron magnetohydrodynamic (EMHD) fluid since characteristic beam times τ satisfy 2π/ωpe,2π/Ωe≪τ≤2π/Ωi (ωpe is the electron plasma frequency and Ωe,i are the electron, ion gyrofrequencies). When the electron collisionality satisfies νe≪Ωe, the linear plasma response is determined by whistler wave dynamics. In this case, current neutralization of the beam is reduced on the time scale for whistler wave transit across the beam. The transit time is inversely proportional to the electron density and proportional to the angle of incidence of the beam with respect to the applied solenoidal field. In the collisional regime (νe&amp;gt;Ωe) the plasma return currents decay on the normal diffusive time scale determined by the conductivity. The analysis is supported by two-and-one-half dimensional hybrid particle-in-cell simulations.

Fast decay of plasma return currents due to whistler waves

The evolution of the return current induced by a charged particle beam in a magnetized plasma is studied. The beam current is perpendicular to the background magnetic field. The return current is shown to depart from the beam along the background magnetic field with a whistler rather than a diffusion or an Alfvén velocity. In a plasma bounded by two conductors the return current oscillates with the whistler period. Analytical expressions for the evolution of the magnetic field and of the plasma return current are derived for a beam with a finite width and with various rise time dependences. When the whistler time is shorter than the rise time of the beam current, the plasma return current does not grow beyond the whistler time.

Ion ring propagation in a magnetized plasma

The propagation of an ion ring in a 2.5 m long, 0.30 m diam magnetized plasma column was studied using an axial array of magnetic probes and fast proton detectors, a microwave interferometer, and a grating spectrometer. The ring propagated with an initial axial velocity 3×106 m/sec, about four times the Alfvén speed in the plasma, and excited damped magnetosonic waves whose peak amplitude depended on the plasma return current. The plasma electrons were heated by about 1 eV in response to the ring, as measured by the Hγ line-to-continuum intensity ratio. This heating is primarily attributed to classical Coulomb collisions, although about 1%–10% can be attributed to the collective ring–plasma interaction. The collective interaction had no measurable effect on the dynamics of the ion ring, consistent with theoretical models, given the beam, plasma, and magnetic-field parameters in the experiment.

The axisymmetric instability of a self-pinched beam with rounded radial density profile

The axisymmetric perturbations (sausage and hollowing modes) of an intense relativistic self-pinched electron beam propagating in a resistive plasma background are studied, especially for a beam with rounded radial density profile. The Bennett profiles are assumed for both the equilibrium beam current Jb(r)=Jb(0) (1+r2/R2b)−2 and plasma return current Jp(r)=−fJb(0) (1+r2/R2p)−2, where Rb and Rp are the characteristic radii of the beam and plasma return currents, respectively. It is further assumed that the electric conductivity σ(r) of the plasma channel is proportional to the return current. For a paraxial electron beam with complete space-charge neutralization by the ambient plasma, the axisymmetric modes can be destabilized by the phase lag between the magnetic field and beam current, even without the plasma return current. The plasma return current significantly modifies the growth rate of the instability such that the ratio of plasma current to beam current (−Ip/Ib=fR2p/ iR2b) largely determines the stability character of the beam. Furthermore, for the same fractional current neutralization f, the modes are highly unstable for a smaller ratio of plasma to beam radius Rp/Rb. As compared to the resistive hose instability, the growth rates for the hollowing mode can be larger than those of the hose mode, while the sausage mode is much stabler than the hose mode. Stability properties are illustrated in detail for various system parameters.