Ohmic Plasma Channel Research Articles

Effect of Multiple Scattering of a Relativistic Electron Beam in a Gas–Plasma Medium on the Dynamics of the Resistive Hose Instability

We consider the effect of the multiple Coulomb scattering on the spatial dynamics of the relativistic hose instability of a relativistic electron beam propagating along an Ohmic plasma channel. It is shown that the enhancement of scattering noticeably suppresses this instability.

Effect of Temporal Current Modulation on the Tracking Force Acting on a Relativistic Electron Beam in an Ohmic Plasma Channel

The effect of the current rise time in a relativistic electron beam pulse on the tracking force exerted by the low-conductivity Ohmic plasma channel on the beam has been analyzed using the “hard” beam model. It is shown using numerical analysis that an increase in the beam current rise time substantially reduces the tracking force considered here.

The Calculation of the Tracking Force in the Evolution of the Resistive Hose Instability of a Relativistic Electron Beam

We have analyzed the tacking force exerted by a low-conductivity Ohmic plasma channel on a relativistic electron beam. It has been shown that, for the given type of evolution of the resistive hose instability of the beam along its pulse, this force substantially depends on the frequency and the increment of the increase in the given instability.

The influence of current neutralization and multiple Coulomb scattering on the spatial dynamics of resistive sausage instability of a relativistic electron beam propagating in ohmic plasma

The influence of the current neutralization process, the phase mixing of the trajectories of electrons and multiple Coulomb scattering of electrons beam on the atoms of the background medium on the spatial increment of the growth of sausage instability of a relativistic electron beam propagating in ohmic plasma channel has been considered. It has been shown that the amplification of the current neutralization leads to a significant increase in this instability, and phase mixing and the process of multiple scattering of electrons beam on the atoms of the background medium are the stabilizing factor.

Equation for the envelope of a relativistic electron beam propagating in a resistive plasma channel during the evolution of resistive hose instability

Kinetic methods are used to derive the transport equations, virial equation, dynamic equilibrium condition, and the equation of the envelope of an axially symmetric paraxial relativistic electron beam propagating in an Ohmic plasma channel during the evolution of resistive firehose instability. The equation of the beam envelope is generalized by taking this instability into account.

Generalization of the Bennett equilibrium condition for a relativistic electron beam propagating in the Ohmic plasma channel and ion focusing regime along an external magnetic field

The problem of formulating the generalization of the Bennett equilibrium condition is considered for a relativistic electron beam propagating in the Ohmic plasma channel, as well as in the ion focusing regime in the presence of an external longitudinal uniform magnetic field. We assume that the electron component of the background plasma is not completely removed from the region occupied by the beam. This equilibrium condition is derived using the mass and momentum transport equations obtained for a paraxial monoenergetic beam from the Fokker–Planck kinetic equation.

Equation of the transverse dynamics of a relativistic electron beam propagating in an ohmic plasma channel under ion focusing conditions

The equation is formulated that covers two regimes: resistive firehose instability and the situation of ion firehose instability evolution at the linear stage of their dynamics. Stabilizing and destabilizing terms in these equations are indicated.

Analytical treatment of the force acting on a relativistic electron beam spreading in dense gas plasma by the ohmic plasma channel

A method is described for the analytical evaluation of the force acting on a relativistic electron beam spreading in dense gas plasma by the ohmic plasma channel. This is useful for the solution of the general definitions for the force of the beam plasma interactions in the case of an arbitrary displacement of the symmetry axis of the plasma channel relative to the corresponding axis of the beam. The accuracy of these procedures is tested and their efficiency illustrated with practical applications, including the computation of the tracking force exerting on a relativistic electron beam by the ohmic plasma channel.

Calculation of force exerted by the Ohmic plasma channel on a relativistic electron beam propagating in a dense gas-plasma medium

The problem on the interaction of an Ohmic plasma channel displaced in the transverse direction with a paraxial azimuthally symmetric relativistic electron beam propagating in a dense gas-plasma medium is considered. The formula for determining the force of the beam-plasma interaction is derived using the “hard” model of the beam and the channel in the case of an arbitrary displacement of the symmetry axis of the plasma channel relative to the corresponding axis of the beam. The forces are calculated in the Bennett and Gauss approximations for the radial profiles of the beam and the channel.

Calculation of the electrostatic tracking force in the transport of relativistic electron beams in Ohmic plasma channels of low conductivity

The interaction force between a paraxial relativistic electron beam and a preformed Ohmic plasma channel of low conductivity is calculated in the electrostatic limit. The dependence of this force on the channel conductivity and the distance from the beam front is found for concrete parameters of the relativistic electron beam and various values of the beam current rise rate.

Calculation of the interaction force between a relativistic electron beam and an Ohmic plasma channel

A formula for calculating the interaction force between a relativistic electron beam and a preformed Ohmic plasma channel with an arbitrary offset of the channel axis from the beam axis is obtained in the case of complete charge neutralization. It is shown that this force is repulsive for radial profiles of the conductivity with a peak on the channel axis.

The tracking force on a relativistic electron beam in an Ohmic plasma channel

The linearized tracking force on an electron beam propagating slightly off axis in an Ohmic plasma channel is calculated. Electron inertial effects are included in Ohm’s law. The channel of conductivity (σ), density (ne), and radius (a) is surrounded by a region of ambient plasma with conductivity (σ0), density (ne0), and radius (b). Enclosing the system is a highly conducting metallic tank. The electromagnetic fields are calculated using the frozen-field approximation of the Maxwell field equations. The fields are expanded into monopole and dipole moments linearized in the small parameter (d/a), where (d) is the beam displacement. The electron beam is assumed to be a rigid cylinder of charge propagating at the speed of light through the channel and is not allowed to respond dynamically to the force.

General Theory of Resistive Beam Instabilities

This paper considers all resistive instabilities of a self-pinched cylindrically symmetric beam of charged particles in a finite or an infinite Ohmic plasma channel. The problem is reduced to an ordinary second-order linear differential equation for the longitudinal component of the perturbed electric field. The equation can be solved for a uniform beam shape, yielding an implicit transcendental equation whose roots define the various modes. We find that for each azimuthal ``quantum number'' m there are two infinite sequences of modes and two exceptional modes, except that some of these modes are missing for m = 0, 1, and 2. In all modes we find stable oscillation at very low and very high frequencies, and instability at intermediate frequencies, the growth rates generally reaching maxima somewhat less than the betatron frequency ωβ. The largest maximum growth rate is in the ``hose'' mode (the only exceptional mode for m = 1), where it is approximately 0.29 ωβ. For a general smooth beam shape, the catalog of modes is similar to that for a uniform beam, except that there also appears a continuous spectrum. It is also proved for general beam shape that at low frequencies the ``hose'' dispersion relation becomes the same as that derived earlier under the assumption of rigid beam displacement; this is not the case at higher frequencies.

The Hose Instability Dispersion Relation

The dispersion relation is obtained for the ``hose'' instability in a modulated beam of charged particles traveling through a finite ohmic plasma channel. For a relativistic beam, the low-frequency mode obeys a dispersion relation of the same form as for the unmodulated beam, but it involves a constant which will have to be obtained by machine computation. For large enough modulation frequency the dispersion relation is identical to that for an unmodulated beam.