Dynamics of beam instability in a finite plasma volume: Numerical experiment

Results are presented from numerical simulations of the dynamics of beam instability in a finite plasma volume (plasma-filled cavity) in a weak magnetic field. It is shown that, in such a system, the low group velocity of the plasma waves excited by an electron beam can result in the generation and amplification of an electric field; strong electron heating in the axial region; and, as a consequence, the generation of a high potential at the axis. The quasistatic radial electric field so produced accelerates ions toward the periphery of the plasma column, forming a directed ion beam with an energy much higher than the thermal energy of the bulk plasma electrons.     

Interaction of an ion bunch with a plasma slab

Charge neutralization of a short ion bunch passing through a plasma slab is studied by means of numerical simulation. It is shown that a fraction of plasma electrons are trapped by the bunch under the action of the collective charge separation field. The accelerated electrons generated in this process excite beam?plasma instability, thereby violating the trapping conditions. The process of electron trapping is also strongly affected by the high-frequency electric field caused by plasma oscillations at the slab boundaries. It is examined how the degree of charge neutralization depends on the parameters of the bunch and plasma slab.     

Excitation of magnetic fields by a circularly polarized laser pulse in a plasma channel

The excitation of quasistatic magnetic fields by a circularly polarized laser pulse in a plasma channel is considered. It is shown that, to second order in the amplitude of the electric field of the laser pulse, circular rotation of the plane of polarization of the laser radiation in a radially nonuniform plasma gives rise to a nonlinear azimuthal current and leads to the excitation of the radial and axial components of the magnetic field. The dependence of the magnetic field distribution over the plasma channel on the spatial dimensions of the pulse and on the channel width is investigated for a moderate-power laser pulse. The structure of the magnetic fields excited by a relativistic laser pulse in a wide plasma channel is analyzed.     

Generation of strong magnetic fields by counterpropagating moderate-intensity laser pulses in a low-density plasma

A study is made of the generation of strong quasistatic magnetic fields by counterpropagating moderate-intensity laser pulses of different frequencies in a low-density plasma. Strong magnetic fields are generated by small-scale large-amplitude plasma waves excited at different frequencies by ponderomotive forces in the interaction region of laser pulses. It is shown that magnetic fields are generated most efficiently under resonance conditions such that the frequency difference between laser pulses coincides with the plasma frequency. The spatial distribution of quasistatic magnetic fields is investigated, and the pattern of the contour lines of the electric current is calculated.     

Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field

The influence of a transverse magnetic field on the characteristics of the positive column of a planar low-pressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuous-medium model, while the ion motion in the ambipolar electric field is described by means of a kinetic equation. Using mathematical transformations, the problem is reduced to a secondorder ordinary differential equation, from which the spatial distribution of the potential is found in an analytic form. The spatial distributions of the plasma density, mean plasma velocity, and electric potential are calculated, the ion velocity distribution function at the plasma boundary is found, and the electron energy as a function of the magnetic field is determined. It is shown that, as the magnetic field rises, the electron energy increases, the distributions of the plasma density and mean plasma velocity become asymmetric, the maximum of the plasma density is displaced in the direction of the Ampère force, and the ion flux in this direction becomes substantially larger than the counter-directed ion flux.     

Decay instability of a laser pulse propagating in a transverse direction in a magnetized plasma

The decay instability of a lser pulse propagating across an external magnetic field in a subscritical plasma is investigated analytically and numerically. It is shown that, when the relaxation of the pulse is taken into account, the hydrodynamic growth rate of the decay instability is slower than that obtained earlier in the constant-amplitude pump wave approximation. The results of numerical simulations by a particle-in-cell method demonstrate that an increase in the amplitude of the parametrically excited waves is accompanied by a decrease in their group velocity; in this case, up to 85% of the laser energy is converted into the energy of the plasma particles. It is found that, under resonance conditions, the magnetic field acts to increase the energy of the accelerated ions that escape from the plasma slab through its front boundary.     

Possible mechanism for radial ion acceleration in a beam-plasma discharge

A mechanism is proposed that can lead to radial ion acceleration in a plasma discharge excited by an electron beam in a relatively weak longitudinal magnetic field. The mechanism operates as follows. The beam generates an azimuthally asymmetric slow potential wave, which traps electrons. Trapped magnetized electrons drift radially with a fairly high velocity under the combined action of the azimuthal wave field (which is constant for them) and a relatively weak external longitudinal magnetic field. The radial electron flux generates a radial charge-separation electric field, which accelerates unmagnetized plasma ions in the radial direction. The ion flux densities and energies achievable in experiments with kiloelectronvolt electron beams in magnetic fields of up to 100 G are estimated.     

Investigation of ion acceleration in an expanding laser plasma by using a hybrid Boltzmann-Vlasov-Poisson model

The acceleration of ions of different species from a plasma slab under the action of a charge-separation electric field driven by hot and cold electrons is studied by using a hybrid Boltzmann-Vlasov-Poisson model. The obtained spatial and energy distributions of light and heavy ions in different charge states demonstrate that the model can be efficiently used to study the ion composition in a multispecies expanding laser plasma. The regular features of the acceleration of ions of different species are investigated. The formation of compression and rarefaction waves in the halo of light ion impurity, as well as their effect on the energy spectrum of the accelerated ions, is analyzed. An approach is proposed that makes it possible to describe the production of fast ions by laser pulses of a given shape. It is shown that the energy of fast ions can be increased markedly by appropriately shaping the pulse. The effect of heating of the bulk of the cold target electrons on the ion acceleration is discussed.     

Charged prticle aceleration by an itense ultrashort electromagnetic pulse excited in a plasma by laser radiation or by relativistic electron bunches

A review is given of theoretical and experimental investigations and numerical simulations of the generation of intense electromagnetic fields in accelerators based on collective methods of charged particle acceleration at rates two or three orders of magnitude higher than those in classical resonance accelerators. The conditions are studied under which the excitation of accelerating fields by relativistic electron bunches or intense laser radiation in a plasma is most efficient. Such factors as parametric and modulational processes, the generation of a quasistatic magnetic field, and the acceleration of plasma electrons and ions are investigated in order to determine the optimum conditions for the most efficient acceleration of the driven charged-particle bunches.     

Nonlinear Right-Hand Polarized Wave in Plasma in the Electron Cyclotron Resonance Region

The propagation of a nonlinear right-hand polarized wave along an external magnetic field in subcritical plasma in the electron cyclotron resonance region is studied using numerical simulations. It is shown that a small-amplitude plasma wave excited in low-density plasma is unstable against modulation instability with a modulation period equal to the wavelength of the excited wave. The modulation amplitude in this case increases with decreasing detuning from the resonance frequency. The simulations have shown that, for large-amplitude waves of the laser frequency range propagating in plasma in a superstrong magnetic field, the maximum amplitude of the excited longitudinal electric field increases with the increasing external magnetic field and can reach 30% of the initial amplitude of the electric field in the laser wave. In this case, the energy of plasma electrons begins to substantially increase already at magnetic fields significantly lower than the resonance value. The laser energy transferred to plasma electrons in a strong external magnetic field is found to increase severalfold compared to that in isotropic plasma. It is shown that this mechanism of laser radiation absorption depends only slightly on the electron temperature.     

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field. Part II

Propagation and amplification of extraordinary electromagnetic waves in a dipole magnetic field in a narrow 3D plasma cavity in which a weakly relativistic electron beam propagates along the magnetic field in the direction of the gradient of the magnetic field strength is investigated. The domain of wave vectors at the starting point for which the wave amplification factors at the output of the density cavity reach their maximum values is found, and the amplification factor as a function of the wave frequency is determined. It is shown that the longitudinal velocity of fast electrons, which enables generation of waves in a broader frequency range, plays an important role in the formation of the spectrum of the auroral kilometric radiation (AKR). In this case, waves with the largest amplification factors at the output of the cavity have frequencies exceeding the cutoff frequency of the background plasma at the wave generation altitude. The global inhomogeneity of the magnetic field and plasma density, which governs the residence time of the waves in the amplification region, plays a key role in the formation of the AKR spectrum. It is shown that this time is the main factor determining the energy of the waves emerging from the source.     

Oscillation spectrum of an electron gas with a small density fraction of ions

The problem is solved of the stability of a nonneutral plasma that completely fills a waveguide and consists of magnetized cold electrons and a small density fraction of ions produced by ionization of the atoms of the background gas. The ions are described by an anisotropic distribution function that takes into account the characteristic features of their production in crossed electric and magnetic fields. By solving a set of Vlasov-Poisson equations analytically, a dispersion equation is obtained that is valid over the entire range of allowable electric and magnetic field strengths. The solutions to the dispersion equation for the m = +1 main azimuthal mode are found numerically. The plasma oscillation spectrum consists of the families of Trivelpiece-Gould modes at frequencies equal to the frequencies of oblique Langmuir oscillations Doppler shifted by the electron rotation and also of the families of “modified” ion cyclotron (MIC) modes at frequencies close to the harmonics of the MIC frequency (the frequencies of radial ion oscillations in crossed fields). It is shown that, over a wide range of electric and magnetic field strengths, Trivelpiece-Gould modes have low frequencies and interact with MIC modes. Trivelpiece-Gould modes at frequencies close to the harmonics of the MIC frequency with nonnegative numbers are unstable. The lowest radial Trivelpiece-Gould mode at a frequency close to the zeroth harmonic of the MIC frequency has the fastest growth rate. MIC modes are unstable over a wide range of electric and magnetic field strengths and grow at far slower rates. For a low ion density, a simplified dispersion equation is derived perturbatively that accounts for the nonlocal ion contribution, but, at the same time, has the form of a local dispersion equation for a plasma with a transverse current and anisotropic ions. The solutions to the simplified dispersion equation are obtained analytically. The growth rates of the Trivelpiece-Gould modes and the behavior of the MIC modes agree with those obtained by numerical simulation.     

Theory of the near-wall conductivity

A model describing the phenomenon of the electron current in a plane plasma slab bounded by parallel dielectric walls in the presence of a homogeneous magnetic field perpendicular to the walls and an electric field oriented along the walls is presented. The current flows along the electric field because of the electron collisions with diffusely scattering walls. The model takes into account the presence of Debye layers and the non-Maxwellian character of the electron distribution function. Collisions in the plasma volume are ignored.     

Experimental modeling of a novel magnetic confinement system: Galathea with a myxine in the shape of a convex polyhedron

A new type of magnetic confinement system—a Galathea with a myxine in the shape of a convex polyhedron—is proposed. The system was modeled experimentally by passing an RF current through the myxine. On the one hand, the myxine acts as an inductor whose electric field ionizes the gas and, on the other, it acts as an RF magnetic confinement system. A steady-state plasma produced and confined in this system is almost spherical in shape. The electron density and specific (per unit volume) glow intensity of the plasma produced are found to be higher than those in conventional helical inductors.     

Efficiency of ion acceleration by a relativistically strong laser pulse in an underdense plasma

A particle-in-cell simulation is used to investigate ion acceleration by a femtosecond laser pulse propagating in an underdense plasma slab. In plasma slabs with different thicknesses, the ions are found to be accelerated by different mechanisms. It is shown that, for laser pulse intensities in the range (5–10)×10¹⁹ W/cm², the ions are accelerated near the plasma-vacuum interface. __________ Translated from Fizika Plazmy, Vol. 27, No. 3, 2001, pp. 225–234. Original Russian Text Copyright ￠ 2001 by Kuznetsov, Esirkepov, Kamenets, Bulanov.     

Characteristic features of electron-ion collisions in strong electric fields

The classical motion of an electron in the Coulomb field of an ion and in a uniform external electric field is analyzed. A nondimensionalization method that makes it possible to study electron motion in arbitrarily strong electric fields is proposed. The possible electron trajectories in the plane of motion in a static field are classified. It is noted that, from a practical standpoint, the most interesting trajectories are snakelike trajectories, which are absent in the problem with a weak external field. An adiabatic approximation for transverse electron motions in quasistatic (strong) fields is constructed. A one-dimensional equation of motion is derived that accounts for transverse electron oscillations and the increase in the effective electron mass as an electron approaches an ion. An analytic model is used to calculate the spectra of bremsstrahlung generated by individual electrons. The calculated results are shown to agree well with the results of direct numerical integration of the basic equations. It is predicted that, at frequencies higher than the frequency of the incident light, pronounced peaks can appear in the spectrum of the transverse dipole moment of an electron; as a result, an electron is expected to effectively emit radiation at these frequencies in the direction of the external field.     

Experimental studies of the behavior of the ion plasma component during disruptive instability in a tokamak

Results are presented from experimental studies of the behavior of the plasma ion component during disruptive instability in the TVD and DAMAVAND tokamaks. It is shown that the ion temperature increases during a major disruption by a factor of 1.5–2. The ions are accelerated predominantly across the magnetic field near the rational magnetic surfaces. Results on the ion acceleration along the magnetic field indicate that disruptions are accompanied by the generation of longitudinal electric fields that are aligned in opposite directions at the plasma periphery and near the plasma axis.     

Charge and energy spectra of fast multicharged ions in a laser plasma

In measuring the charge and energy spectra of the ions of a single-element laser plasma, in addition to thermal ions, fast multicharged ions are recorded that are accelerated by the electric field of laser radiation in the region of the critical plasma density. The charge and energy spectra of Co ions with the charge numbers z=1–3 are measured at laser intensities of q=5×10¹¹–10¹² W/cm². The energy spectra of these ions are broad and are located on the high-energy side (z _max=3, E>5.0 keV) with respect to the thermal ions (z _max=9, E<4.0 keV). The increase in q to 10¹⁴ W/cm² results in an increase in the charge number of both thermal and fast ions.     

Generation of quasistatic magnetic fields in the interaction of counterpropagating laser pulses in a low-density plasma

The effect of generation of quasistatic magnetic fields in the interaction of counterpropagating moderate-intensity laser pulses in a low-density plasma is considered. It is shown that the onset of strong magnetic fields is attributed to small-scale large-amplitude plasma waves excited in the region of interaction of laser pulses under the action of the averaged ponderomotive forces. The spatial distribution of quasistatic magnetic fields is investigated, as well as the structure of the magnetic-field and current lines.     

Dynamics of accelerated ions in coronal loops and model of a gamma-ray source

The dynamics of ions accelerated to energies of 10–100 MeV/nucleon in an electric field of ～0.01–0.1 V/cm, which has a component directed along the magnetic field of solar coronal loops with a characteristic size of ～100000 km, is considered. The motion of fast ions trapped in a current-carrying magnetic loop that has a magnetic mirror at its base (the mirror trap model) is analyzed. The applicability of the obtained theoretical results to interpret gamma-ray bursts that, according to the data of the RHESSI space observatory, occurred on July 23, 2002 and October 28, 2003, is discussed. In those two bursts, a single and a pair gamma source displaced relative to the hard X-ray sources were localized in the 2.223-MeV neutron-capture line. On the basis of complex analysis of multi-wavelength (X-ray, gamma-ray, and optical) observations and the data on fast solar protons, a new topological model of the source of accelerated particles (of the mirror trap type) and a new scenario of the event that occurred on July 23, 2002 are proposed. Evidence of the possibility of particle acceleration by the electric field in coronal mass-ejection loops during large solar flares is obtained. The simulation results indicate that the gamma-ray source in the excitation lines (4.1–6.7 MeV) should coincide with the region where the accelerated ions interact with the background plasma of the solar atmosphere above the spot of the flare active region.