Resistive Hose Research Articles

Resistive hose modes in tokamak runaway electron beams

Beams of energetic runaway electrons are generated during disruptions in tokamaks, and fluid models are used to study their effects on macroscale dynamics. Linear computations of a massless, runaway electron beam coupled to MHD plasma show that resistive hose instabilities grow faster than tearing modes at large resistivity. Eigenvalue results with reduced models of the resistive hose instability are compared with results from the full MHD and beam system, showing that the resistive hose decouples from any plasma response. An estimate of plasma temperature at which growth of the resistive hose dominates tearing for post-disruption DIII-D plasma parameters is in a physically relevant regime.

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.

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.

Simulation of the dynamics of resistive hose instability of a relativistic electron beam propagating in a resistive plasma channel with arbitrary conductivity

The spatial dynamics of the resistive hose instability of a relativistic electron beam has been studied for the case when the charge neutralization time is much longer, on the order of, or much shorter than the current compensation time. It has been found that the growth of this instability has the highest increment when the charge neutralization time is on the order of skin time.

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 equation for the quasi-stationary relativistic electron beam envelope to the case of Resistive Hose instability

The statement of an equation for the envelope of a quasi-stationary relativistic electron beam experiencing Resistive Hose instability is considered. The well-known Nordsieck equation is generalized to the case of Resistive Hose instability using analytical methods.

Effect of the return plasma current radial profile on the dynamics of resistive hose instability of a relativistic electron beam propagating in a dense gas-plasma medium

The effect of the return plasma current with a characteristic radius differing from the relevant radius of the current density in a relativistic electron beam on the dynamics of the resistive hose instability of the beam is analyzed. The equations are derived for the linear stage of instability evolution. It is shown that when the return plasma current is broader in the radial direction (as compared to the beam), the resistive hose instability becomes noticeably weaker.

Suppression of resistive hose instability in a relativistic electron–positron flow

This paper presents the effects of electron-positron pair production on the linear growth of the resistive hose instability of a filamentary beam that could lead to snake-like distortion. For both the rectangular radial density profile and the diffuse profile reflecting the Bennett-type equilibrium for a self-collimating flow, the modified eigenvalue equations are derived from a Vlasov-Maxwell equation. While for the simple rectangular profile, current perturbation is localized at the sharp radial edge, for the realistic Bennett profile with an obscure edge, it is non-locally distributed over the entire beam, removing catastrophic wave-particle resonance. The pair production effects likely decrease the betatron frequency, and expand the beam radius to increase the resistive decay time of the perturbed current; these also lead to a reduction of the growth rate. It is shown that, for the Bennett profile case, the characteristic growth distance for a preferential mode can exceed the observational length-scale of astrophysical jets. This might provide the key to the problem of the stabilized transport of the astrophysical jets including extragalactic jets up to Mpc ($\sim 3\times 10^{24}$ cm) scales.

Resistive hose growth of intense ion beams propagating in air

The growth of the resistive hose instability for intense proton beams is examined using three-dimensional particle-in-cell simulations. The simulation results are compared with a time-dependent model of resistive hose growth that uses a spread-mass formulation and a time-dependent conductivity model. Radius tailoring of the beam head is shown to suppress high-frequency instability growth. In addition, the effects of a reduced-density plasma channel on the growth of the resistive hose instability is calculated.

A theory of resistive hose instability in intense charged particle beams propagating through background plasma with low electron collision-frequency

Stability properties of the resistive hose instability is investigated for a rounded current-density profile of a charged particle beam propagating through a background plasma where the electron collision time (1//spl nu//sub c/) is comparable to or longer than the magnetic decay time (/spl tau//sub d/). The eigenvalue equation is derived based on the energy group model, including the stabilizing influence of a finite magnetic decay time. The dispersion relation of the resistive hose instability in a charged particle beam with an arbitrary current density profile is derived, assuming that the eigenfunctions can be represented by the rigid displacement of the self magnetic field in the plasma. Stability analysis for perturbations propagating through the beam pulse from its head to tail is carried out for an arbitrary current profile of the beam. It is shown from the stability analysis that the width of the range /spl Omega//sup 2/ corresponding to instability decreases drastically as the value of parameter /spl nu//sub c//spl tau//sub d/ decreases from infinity to zero, thereby being a very narrow bandwidth of instability. It is also shown for arbitrary current profile that any perturbation with frequency /spl Omega/ higher than the maximum betatron frequency /spl omega//sub /spl beta/m/ is stable. Here, /spl Omega/ is the Doppler-shifted frequency seen by beam particles.

Effect of the parameters of the plasma channel produced by a high-current relativistic electron beam in dense gaseous media on the beam transportation stability

Results are presented from experimental studies of the time evolution of the plasma channel produced by a high-current electron beam (with an electron energy of Ee = 1.1 MeV, a beam current of Ib = 24 kA, and a pulse duration of t = 60 ns) in helium, nitrogen, neon, air, argon, krypton, xenon, and humid air (air: H2O) at pressures from 1 to 760 Torr. It is shown that, in gases characterized by a small ratio of the collision frequency to the gas ionization rate ui, the electron beam produces a broad high-conductivity plasma channel, such that Rb/Rp < 1, where Rb and Rp are the beam and channel radii, respectively. As a result, large-scale resistive hose instability is suppressed.

Collective instabilities and beam-plasma interactions in intense heavy ion beams

This paper presents a survey of the present theoretical understanding of collective processes and beam-plasma interactions affecting intense heavy ion beam propagation in heavy ion fusion systems. In the acceleration and beam transport regions, the topics covered include discussion of the conditions for quiescent beam propagation over long distances; the electrostatic Harris-type instability and the transverse electromagnetic Weibel-type instability in strongly anisotropic, one-component non-neutral ion beams; and the dipole-mode, electron-ion two-stream instability driven by an (unwanted) component of background electrons. In the plasma plug and target chamber regions, collective processes associated with the interaction of the intense ion beam with a charge-neutralizing background plasma are described, including the electrostatic electron-ion two-stream instability, the electromagnetic Weibel instability, and the resistive hose instability. Operating regimes are identified where the possible deleterious effects of collective processes on beam quality are minimized.

Effects of the Plasma Conductivity on Transverse Instabilities in High-Intensity Ion Beam

Summary form only given, as follows. Intense ion beams produced in high energy accelerators and transport systems have wide range applications, including basic scientific research, spallation neutron sources, nuclear waste transmutation, and heavy ion fusion, to mention a few examples. Ion beams propagating through preformed plasma may be subject to various instabilities that can cause deterioration of the beam quality. The most deleterious instabilities in the intense ion beams propagating through a preformed plasma channel are the electron-ion two stream and the resistive-hose instabilities, which disturb the ion beam sideway, thereby pushing it out of channel and eventually losing it. The electron-ion two stream instability occurs in collisionless plasma, developing a dipole oscillation between the beam and plasma column segments. This dipole oscillation caused by the Coulomb force overshoots and grows. On the other hand, when a current-carrying beam moves through conducting plasma, its self-magnetic field may follow the beam with a delay time called the magnetic decay time. The magnetic field lines are frozen into the plasma, pulling back the distorted beam segment if the plasma is highly conducting. This restoring mechanism, which leads to the resistive hose instability, overshoots and grows due to the motionless resistive plasma medium. Basic properties of these two instabilities will be presented. The transformation from the two-stream instability to the resistive-hose instability will be traced by properties of the preformed plasma channel.

Effects of electron collisions on the resistive hose instability in intense charged particle beams propagating through background plasma

The dispersion relation for the resistive hose instability in a charged particle beam with a flattop density profile is derived from the linearized Vlasov-Maxwell equations. Stability properties of the resistive hose instability where the perturbations are initiated at the beam entrance are investigated. In particular, the complex eigenfrequency $\ensuremath{\Omega}$ in the dispersion relation is expressed as a function of the real oscillation frequency $\ensuremath{\omega}$ of the excitation at the beam entrance. As expected, the growth rate $\mathrm{Im}\ensuremath{\Omega}={\ensuremath{\Omega}}_{i}$ decreases rapidly as the conducting wall approaches the beam (${r}_{w}/{r}_{b}\ensuremath{\rightarrow}1$). The growth rate also decreases substantially as the frequency ratio $\ensuremath{\omega}/{\ensuremath{\nu}}_{c}$ increases, where ${\ensuremath{\nu}}_{c}$ is the electron collision frequency. Stability properties for perturbations propagating through the beam pulse from its head to tail are also investigated. In this case, the growth rate $\mathrm{Im}\ensuremath{\omega}$ is calculated in terms of the real oscillation frequency $\ensuremath{\Omega}$ of each beam segment. It is shown that the resonance frequency $\ensuremath{\Omega}={\ensuremath{\Omega}}_{r}$ corresponding to the infinite growth rate detunes considerably from the betatron frequency ${\ensuremath{\omega}}_{\ensuremath{\beta}}$ of the beam particles. It is also found that the bandwidth corresponding to instability is narrow when the plasma electron collision time ($1/{\ensuremath{\nu}}_{c}$) is long compared with the magnetic decay time (${\ensuremath{\tau}}_{d}$).

Computation of the tracking force acting on a relativistic electron beam propagating in a conducting waveguide under the ohmic and ion-focused regimes

The force of interaction between a relativistic electron beam deflected by resistive hose instability and the eddy current induced in a tubular plasma channel of finite conductivity is computed. Dependences of the force on channel ohmic conductivity and current rise time in a beam pulse are studied. For a beam propagating through a perfectly conducting waveguide under the ion-focused regime, the interaction of the beam with the ion-channel electrostatic image on the waveguide wall is studied for the case when the beam and the channel are deflected from the waveguide axis as a result of ion hose instability. The dependence of the force on both deflection amplitudes is ascertained for the nonlinear phase of instability. It is demonstrated that the force under study may become comparable to the beam-channel interaction force if the deflections are large.

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.

Emittance tailoring of electron beams for propagation in dense gas

An intense relativistic electron beam injected into dense gas characteristically propagates in a self-pinched mode but is susceptible to the resistive hose instability. This convective instability typically leads to large amplitude beam motion and the disruption of propagation. Theory and computation suggest that, although resistive hose cannot be completely suppressed, its convective growth can be reduced by varying the average betatron oscillation frequency from head to tail in the beam pulse. We report here on experiments designed to implement this variation by tailoring the beam emittance using an ion-focused regime ‘‘conditioning’’ cell. Conditioning effectiveness is assessed by using measured beam quantities to evaluate a detuning parameter η(t). This information is correlated with beam propagation measurements to determine the optimum conditioning for resistive hose suppression.

Use of an active wire Bθ cell for electron beam conditioning

The propagation of intense, relativistic electron beams in air is subject to the resistive hose instability. Conditioning the beam prior to injecting it into the air can extend its range by reducing the hose growth rate and by reducing the initial spatial perturbations that seed the hose instability. Experiments have been performed using the SuperIBEX accelerator (Ipeak=10–30 kA, E=4.5 MeV, 40 ns full width at half-maximum) to develop conditioning cells that suppress the hose. This paper describes the performance of an active wire Bθ cell that is used in conjunction with an ion focused regime (IFR) cell. The IFR cell detunes the instability by producing a head-to-tail radius taper on the beam. The wire cell maintains this radius taper while producing an emittance taper that is necessary to suppress the hose growth. In addition, the wire cell reduces the initial beam perturbations through the anharmonic centering force associated with the wire current and its azimuthal magnetic field Bθ. The ability of the Bθ cell to reduce the beam offset with a minimal increase in the beam radius gives it several advantages over the use of a simple, thick scattering foil to perform the radius taper to emittance taper conversion. The SuperIBEX beam propagation distance, in terms of the betatron oscillation scale length, was extended to ∼10λβ using these cells.

Controlling the resistive hose instability in relativistic electron beams

The resistive hose instability has long been recognized as the major impediment to the propagation of intense, relativistic electrons beams in dense gas. However, hose is a convective instability, and therefore its growth is limited by the length of the beam pulse, the local growth rate, and the speed at which the instability convects through the pulse. The convective speed and the growth rate depend on the beam and plasma parameters, and these vary strongly from beam head to tail. In this paper, hose theory is reformulated to incorporate these variations, and the reformulated model is then used to compute the maximum hose growth possible in a given beam pulse. In air, the model predicts that hose grows by many orders of magnitude when the beam current is less than 10 kA or has a rise time more than a few nanoseconds long. But the growth is predicted to be less than a factor of 20 if the current is 50 kA or more, the rise time is subnanosecond, and the beam radius is properly tapered from head to tail. The model is supported by extensive numerical simulations and is in general agreement with available experimental data. Many of the issues discussed here may have application to other instabilities as well.

High-power electron-beam transport in long gas cells from 10−3 to 103 Torr nitrogen

Measurements and analyses show that the 13 TW, pulsed Hermes-III [J. J. Ramirez, Proceedings of the 1989 Particle Accelerator Conference, Chicago, 1989 (IEEE, New York, 1989), p. 1446] electron beam, with current near the Alfvén limit, has two regimes of stable transport: a low-pressure window (between ∼1 and ∼100 mTorr) that is dominated by propagation in the semicollisionless IFR (ion-focused regime), and a high-pressure window (between ∼1 and ∼100 Torr) that is dominated by propagation in the resistive CDR (collision-dominated regime). Below ∼1 mTorr, there is insufficient ionization to confine the beam; between the windows, the two-stream and hollowing instabilities disrupt propagation; and above ∼100 Torr, the resistive hose instability degrades propagation.