Current-carrying Plasma Column Research Articles

Production of energetic protons, deuterons, and neutrons up to 60 MeV via disruption of a current-carrying plasma column at 3 MA

Acceleration of ions to multi-MeV energies is investigated in various plasma devices to better understand processes in astrophysical plasmas and to develop efficient accelerators for a variety of applications. This paper reports the production of proton, deuteron, and electron beams in a z-pinch—a cylindrically symmetric plasma column that is compressed by its own magnetic field. For this work, the GIT-12 pulsed-power generator was used to drive a novel configuration of z-pinch that dramatically enhanced ion acceleration associated with disruption of the current by instabilities in the compressed plasma. During the disruption of 3 MA current, hydrogen ions were accelerated up to at least 50 MeV, which is almost a hundred-times the ion energy provided by the generator driving voltage of 0.6 MV. Under optimal conditions, the total numbers of hydrogen ions with energies above 20 and 50 MeV were 4 × 1013 and 1011, respectively. Accelerated deuterons produced one 20 ns (full width at half maximum) pulse of fast neutrons via D(d, n)3He and other nuclear reactions. A maximum neutron output of (1.0 ± 0.2) × 1012 neutrons/sr was observed downstream, i.e., in the anode to cathode direction. In this direction, the maximum neutron energy reached 58 ± 7 MeV. Both ion and neutron beams in our experiment reached an end-point energy of about 60 MeV, which is the highest value observed in pulsed-power devices. A localized peak voltage of ≳60 MV was driven by the inductive energy that was stored around the plasma column and that was extracted during a sub-nanosecond current drop. Considering the natural occurrence of current-carrying columns in laboratory and space plasmas, the current interruption observed in z-pinches could represent a more general physical process that contributes to the efficient conversion of magnetic energy into the energy of particle beams in various plasmas.

Phenomenological theory of the kink instability in a slender plasma column

In this paper we are concerned with the kink instability of a current-carrying plasma column whose radius a is much smaller than its length L. In the limit a⪡L, one can consider the column as a thin filament whose kinking can be adequately described simply by a two dimensional 2D displacement vector, ξx=ξx(z,t); ξy=ξy(z,t). Details of the internal structure of the column such as the radial distribution of the current, density, and axial flow can be lumped into some phenomenological parameters. This approach is particularly efficient in the problems with nonideal (sheath) boundary conditions (BC) at the end electrodes, with the finite plasma resistivity, and with a substantial axial flow. With the sheath BC imposed at one of the endplates, we find instability in the domain well below the classical Kruskal-Shafranov limit. The presence of an axial flow causes the onset of rotation of the kink and strong axial “skewness” of the eigenfunction, with the perturbation amplitude increasing in the flow direction. The limitations of the phenomenological approach are analyzed and are related to the steepness with which the plasma resistivity increases at the plasma boundary with vacuum.

Bifurcation of the equilibrium of a current-carrying plasma column

The classical (for the Grad-Shafranov equation) formulation of the equilibrium problem for a cylindrical current-carrying plasma column is shown to admit multiple solutions. The multiple solutions are bifurcational in character and appear due to the nonlinearity of the equilibrium equation. This was demonstrated analytically using a stepped current profile as an example. Bifurcational solutions found for the cylindrical case survive in toroidal geometry too.

Stability of a finite-length screw pinch revisited

The ideal magnetohydrodynamic stability of a cylindrical screw pinch (i.e., a current-carrying plasma column embedded into an external axial magnetic field) has been considered in the past in great detail. However, the majority of these studies pertain, in fact, to an infinitely long pinch, where the axial eigenmodes can be represented as exp(ikz). The finite length is then accounted for by assigning a specific value to k, k=2π/L, with L being the distance between the electrodes; in this way, one recovers the familiar Kruskal–Shafranov (KS) stability condition. In the present paper it is emphasized that the solution of the exp(ikz) type cannot satisfy the boundary conditions at the conducting end plates. Previous papers on this subject are reviewed. An effective technique that allows one to analytically obtain stability criteria in the long-thin approximation is developed. Even in this (“long-thin”) case substantial deviations from the KS condition are found. In the general case, a convenient representation is obtained for the Green’s functions that express perturbations both inside and outside the plasma in terms of the radial displacement of the plasma boundary. These expressions are then used in combination with the energy principle to evaluate corrections to the long-thin approximation.

Spectral dependence, efficiency and localization of non-inductive current drive via helicity injection by global Alfvén waves in tokamak plasmas

A systematic study of non-inductive current drive via helicity injection by global Alfven eigenmode (GAE) waves is carried out. For illustration, the first radial mode of the discrete resonant GAE spectrum is considered. The following aspects are given special attention: spectral analysis, radial dependence and efficiency - all of these as functions of the characteristics of the waves launched by an external, concentric antenna (i.e. wave frequency and poloidal and toroidal wavenumbers). The tokamak plasma is simulated by a current-carrying cylindrical plasma column surrounded by a helical sheet current and situated inside a perfectly conducting shell, with incorporation of equilibrium (simulated) toroidal field, magnetic shear and a relatively large poloidal magnetic field component. Within the framework of low-β MHD model equations and for typical tokamak physical parameters, the following basic results are obtained: (1) in the range of poloidal wavenumbers -3 ≤ m ≤ 3 and toroidal wavenumbers -20 ≤ n ≤ 20, resonant GAE peaks below the Alfven continuum are found; (2) the power absorption (P), current drive (I) and corresponding frequency of the GAE modes depend strongly on the sets of (m, n) values considered; (3) the 'net' current drive is positive (i.e. flows in the direction of the equilibrium current j oz ) for m = -1, -2, -3 and -20 ≤ n ≤ -1 as well as for m = +1, +2, +3 and n > 10; (4) in the cases m = -1, -2, -3, the efficiency of current drive, I/P, increases with |m| and I/|n|; (5) the radial localization of the current drive in each of the cases considered is determined and tabulated.

Extragalactic jet collimation due to Cherenkov damping of discrete Alfvén waves

We have shown that discrete Alfvén waves can drive noninductive electric current at the level necessary to explain the observation, via radiotelescope, of extragalactic jet (EJ) collimation. The EJ is modeled as a cylindrical current carrying plasma column surrounded by vacuum [external EJ medium], with L >> a where L and a are the EJ length and radius, respectively. Discrete Alfvén waves (DAW) are global Alfvén modes which propagate disturbing all the plasma column. They can be described by the inclusion of finite ion cyclotron frequency and/or the equilibrium plasma current.

Discrete spectra of compressional Alfvén eigenmodes in inhomogeneous magnetohydrodynamic plasma

The spectrum of the compressional Alfvén eigenmodes in a magnetohydrodynamic (MHD) current-carrying inhomogeneous plasma column is obtained analytically. A MHD model that is adequate for calculating the compressional Alfvén spectra in large tokamaks like the Joint European Torus (JET) [Plasma Physics and Controlled Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 27] and Tokamak Fusion Test Reactor (TFTR) [Plasma Physics and Controlled Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 9] is employed. It is shown that the radial nonuniformities of the plasma density give rise to various types of localization of the eigenmodes. Thus, the global, near-axis, near-wall, and annulus spectra are identified and studied. The eigenfrequencies and domains of localization of the various eigenmodes, as well as their range of existence in parameter and wavelength space, are determined and investigated. The effects of finite ion gyrofrequency on the MHD eigenmodes are examined, and a perturbation scheme for calculating the modified eigenfrequencies and localization domains is presented. Numerical calculations of a set of near-axis eigenmodes for the JET parameters is given as an example for the applicability of the MHD model. Finally, the relevancy of the eigenmodes to plasma heating in large tokamaks is discussed.

On the interpretation of diamagnetic loop measurements for a current-carrying plasma column in a conducting chamber

An expression is derived for the signal of a magnetic loop encircling a plasma column inside a conducting chamber with nonuniform current distribution over the plasma cross section. The plasma with radius much smaller than the length of the column is assumed to be in a quasistationary force-balanced state. The ratio of the paramagnetic component to the diamagnetic component of the signal is shown to be independent of the loop radius. Both components increase as the loop radius decreases from the chamber radius to the plasma radius. From the derived expressions, the paramagnetic component of the signal is calculated numerically for several current distributions including those of interest for the experiments. At a given total current, the paramagnetic component of the signal may vary considerably, which generally has to be taken into account in interpreting experimental data. The results of the calculations are used to process the data obtained in the experiments on the SPIN plasma device [Knyazev et al., ‘‘Characteristics of plasma produced by a linear discharge in the metal chamber of the SPIN device,’’ J. Tech. Phys. 63, 49 (1993) (in Russian)].

A Z-Pinch Plasma Lens for Focusing High-Energy Particles in an Accelerator

The high azimuthal magnetic field of a current-carrying plasma column (z-pinch) can be used to collect and focus high-energy charged particles in accelerators. The beam optics and the apparent advantages of such a linear lens compared with conventional focusing devices, such as magnets and magnetic horns, are described. When a plasma lens shall be operated in routine accelerator runs, the physics of the plasma dynamics must be largely understood and the technology has to be mastered. The results of plasma dynamics measurements and of long-term behavior tests with a plasma lens for antiproton collection are reported. The problems of the plasma dynamics control and of the plasma-wall interaction are discussed in view of the envisaged performance for antiproton collection.

On positional stability of current-carrying plasma in a helical winding

The average force acting on a current-carrying plasma column is calculated when a straight multipolar helical winding is displaced laterally with respect to the plasma, whose average position is kept fixed by a uniform external transverse magnetic field Bx. This nonsymmetric equilibrium problem is solved for force-free j/B=const plasmas by Fourier-analyzing plasma and vacuum fields into helical harmonics and numerically solving the free boundary interface for their amplitudes. In the stellarator limit the average helical force is as predicted from stellarator expansion theory. In the new OHTE limit, both l=2 and l=3 reversed pitch pinches are repelled from the helix. A simple explanation is offered in terms of plasma diamagnetism to the helical field.

Spectrum of low-frequency, nonaxisymmetric oscillations in a cold, current-carrying plasma column

The spectrum of low-frequency, m= ±1 oscillations in a cold, collisionless, cylindrical plasma comprises the frequencies of the lowest radial eigenmodes and the surface modes of the fast magnetosonic wave, all the global eigenmodes of the Alfvén wave (ion-cyclotron wave), and the Alfvén continuum. The spectrum of a homogeneous, currentless plasma cylinder is obtained from an analytical dispersion relation. This spectrum is compared with numerically obtained spectra of nonuniform plasmas with and without axial current. The connection of the magnetohydrodynamic (MHD) kink and internal kink instabilities with the global eigenmodes of the Alfvén wave is evidenced. Among all the modes of the magnetosonic wave which have frequencies in the Alfvén continuum, the (m= −1, k<0) -surface mode is the best candidate for antenna–plasma coupling because its conversion layer is located well into the plasma interior.

Additional stability regions in a plasma column with an inflection point

Describes the open ended device with a nonplanar magnetic axis. A system with a nonplanar axis has its own merits compared with a planar axis. An additional stability region, which is one of the characteristics features for this system, has been found out experimentally in a current-carrying plasma column. This region can be realized only in such a way as an additional current with a significant fast rise time is superposed to a current-carrying stable plasma column.

Magneto-acoustic oscillations as a plasma diagnostic technique for a current-carrying plasma column

Magneto-acoustic oscillations were excited in a non-uniform, current-carrying plasma column. Measurements of the oscillating axial magnetic flux at a number of excitation frequencies were used to determine the equilibrium plasma properties. In agreement with previous theoretical studies, the radial profile of the plasma density is shown to be accurately determined, while it is not possible to obtain detailed information on the radial profile of the equilibrium magnetic field.

MHD stability of a current-carrying curved plasma column with an inflection point

Describes the open ended device with a non-planar magnetic axis of which the torsional angle can be changed easily. It has been pointed out theoretically that the stability region for MHD type instability of the current-carrying plasma in a system with a non-planar magnetic axis differs from that of Tokamak. It is shown experimentally that the condition where the m=1 instability occurs in an open ended system with a non-planar axis is different from that with a planar one. And the observed stability region is shifted from that which is calculated in a linear approximation.

Magnetoacoustic oscillations in a finite-beta current carrying plasma column

Forced magnetoacoustic oscillations in a fully ionized, non-uniform, current carrying plasma column of finite beta are treated theoretically. The results of numerical calculations are given for the specific case of diffuse pinch equilibrium configurations. It is found that, for these configurations, the amplitude of the axial component of the oscillating magnetic field is enhanced and the frequency at which magnetoacoustic resonance occurs is raised. It is also found that the presence of an equilibrium axial current produces a substantial azimuthal component, in addition to the axial component, of the oscillating magnetic field.

Magneto-acoustic oscillation in a current carrying plasma column

Magneto-acoustic oscillation in a current carrying plasma column

High-frequency Surface Waves in a Current Carrying Hot Plasma Column

Abstract The propagation of high-frequency axially-symmetric surface waves along a current-carrying hot plasma column in a glass tube is investigated by means of a kinetic plasma model. The wave spectrum and the wave damping rate are obtained. Our results agree with the experimental data for surface wave propagation in a gas-discharge plasma at low pressures. It is found that the wave damping is mainly due to the Landau mechanism.

Magneto-acoustic oscillations in a current carrying plasma column

The forced radial magneto-acoustic oscillations in a partially-ionized, low- beta plasma column with non-uniform densities, temperature and axial current are investigated theoretically. By using a method of successive approximations to include resistive and viscous dissipations, the description of these oscillations has been reduced to the solution of a second order differential equation in the axial magnetic field disturbance bz(r). A detailed numerical solution is presented for a case where the plasma carries a force-free current and the dissipation is resistive. The steady current enhances the magnetic field amplitudes at magneto-acoustic resonance.

1259. Surface wave propagation along a current-carrying warm plasma column: A Shivarova et al,J Phys D: Appl Phys, 8 (4), 1975, 383-393

1259. Surface wave propagation along a current-carrying warm plasma column: A Shivarova et al,J Phys D: Appl Phys, 8 (4), 1975, 383-393

Positional Instabilities in a Tokamak with a Resistive Shell

The investigation of positional instabilities, that is, vertical displacement and horizontal expansion of the plasma loop, is extended to a tokamak with a resistive shell. The shell current induced by a small displacement of the current-carrying plasma column produces a restoring force, which contributes to the stabilization. The quantitative analysis of the effect due to the shell shows that the finiteness of the minor radius of the plasma column reduces the effective skin time of the shell τs from the intrinsic one. Consequently it is shown that although the stability condition is not altered, a resistive shell restrains the growth rate of the instability to the order of τs-1, in a wider region than the stable one.