Mirror Machine Research Articles

Warm plasma effects on drift cyclotron loss cone mode

Although plasma density gradients in mirror machines are larger than the theoretical threshold for the drift cyclotron loss cone instability, turbulence is experimentally observed only at low harmonics of the ion cyclotron frequency. The evolution of the drift cyclotron loss cone instability as the loss cone velocity distribution is progressively filled with a warm Maxwellian component is studied. The addition of the warm plasma results in both a lowering of the growth rate and a distortion and narrowing of the frequency spectrum. Under conditions typical of an almost filled loss cone, the numerical result shows that the growth rate is largest for the lower ion cyclotron harmonics and is quite consistent with experimental observations.

Concept of Circulatory Mirror Reactor

A new type fusion reactor is proposed. The reactor consists of four identical mirror machines each of which is equipped with a plasma-neutral particle converter. The mirror machine is asymmetric so that the magnetic field of the one end of the machine is larger than that of the other end. So, the plasma trapped in the mirror machine is lost through the end of weaker field. The plasma flux lost through the end enters the plasma-neutral particle converter where ions of the plasma aquire surplus energy and, then, change into neutral particles by charge exchange collision in a gas chamber. The neutral particle beam from the plasma-neutral beam converter is injected into the next mirror machine through the entrance port attached at the side of the machine. The ion confinement time of the reactor is expected to be several times longer than that of each mirror machine composing the reactor. Since the energy which is necessary to compensate the energy loss from the reactor is supplied to the ions during their fleight in the plasma-neutral particle converter, it is not necessary to equip the reactor with any neutral beam injector.

Potential-confined cold plasma stabilization of loss-cone modes in mirror machines

The analysis of cold plasma stabilization of the drift-cyclotron-loss-cone mode in mirror machines is extended to conditions in which the cold plasma is confined by a weak local minimum in the ambipolar potential. These conditions allow stabilization with less electron energy drain than simple axial flow of cold plasma. Scaling laws are derived for the required cold plasma flux, the resulting fluctuation induced ion diffusion, the steady state electron temperature, and the trapped-ion lifetime.

Stochastic acceleration by an obliquely propagating wave-An example of overlapping resonances

A simple problem exhibiting intrinsic stochasticity is treated: the motion of a charged particle in a uniform magnetic field and a single plane wave. Detailed studies of this wave-particle interaction show the following features. An electrostatic wave propagating obliquely to the magnetic field causes stochastic motion if the wave amplitude exceeds a certain threshold. The overlap of cyclotron resonances then destroys a constant of the motion, allowing appreciable momentum transfer to the particles. A wave of large enough amplitude would thus suffer severe damping and lead to rapid heating of a particle distribution. The stochastic motion resembles a diffusion process even though the wave spectrum is monochromatic. The methods of this paper should be useful for other problems showing stochasticity such as superadiabaticity in mirror machines, destruction of magnetic surfaces in toroidal systems, and lower hybrid heating.

Ion temperature gradient driven drift cyclotron instabilities

The role of ion temperature gradient driven drift cyclotron instabilities in both mirror machines and tokamaks is examined. For a completely filled loss cone, reversed temperature and density gradients are necessary for instabilities; however, this inverted profile requirement is relaxed as the fill of the loss cone is decreased and all profiles are unstable for an empty loss cone.

Electron and ion escape over a potential barrier in a mirror field

The problem of calculating the electron loss rate and the corresponding energy loss rate from a magnetic mirror machine having a positive potential has been examined and solved to a reasonable approximation by Pastukhov (1974). This approximation is followed to produce particle and energy confinement times for ions which can be readily utilized in the study of plasma confinement in tandem mirrors. It is shown that a single additional parameter, labeled C, can be incorporated into the appropriate equations to make them equally applicable to electrons and ions; C=1 for electrons and C= square root 2 for ions.

Fusion Reactor Design-II (Report on the Second IAEA Technical Committee Meeting and Workshop, Madison, 1977)

A summary is given of the experimental, demonstration and commercial fusion reactor concepts presented at the Second IAEA Technical Committee Meeting and Workshop on Fusion Reactor Design. The potential role of fusion power as an inexhaustible energy source is discussed, the advances and trends in fusion reactor design assessed, and the major conclusions and recommendations of five workshop groups given.At present, designs for tokamaks are most heavily represented, with the emphasis on near-term reactor studies. Conceptual commercial reactors are becoming compact, high-power-density units. Reactor concepts are also presented for Q-enhanced mirror machines, alternate magnetic fusion concepts, and laser-and electron-beam-driven inertial confinement reactors. The fusion-fission hybrid concepts open up several approaches to fusion power, and special-topic papers cover technology problems and fusion commercialization.

Nonadiabaticity in mirror machines

An analytic technique for calculating magnetic-moment jumps Δμ of particles in magnetic traps, previously derived for particular two-dimensional vacuum fields, is generalized to nonvacuum fields of arbitrary complexity and applied to high-β mirror machines. The size of a jump depends on the behavior of the magnetic-field strength B (s) near the singularities of B in the complex s plane, where real s measures position along a field line. It is demonstrated that an intrinsic complication of mirror-machine magnetic configurations is the presence of multiple singularities of B, which become closely spaced for field lines near the axis. An expansion in r2 is used to determine Δμ in the closely spaced regime. The analytic theory is compared with results from a particle-orbit code for several axisymmetric nonvacuum fields, and is found to be in excellent agreement in both the well separated and closely spaced singularity regimes. Finite-β effects are examined using axisymmetric model fields derived from the long, thin equilibrium approximation, with parameters representative of present (2XIIB) and future (MFTF) mirror experiments. It is shown that increasing β appreciably lowers the maximum energy at which particles are confined. The effect is particularly significant if the plasma length is small compared with the vacuum field axial scale length and if the gyroradius is small compared with the plasma radius. The degradation is substantially reduced when the gyroradius at the energy limit is comparable to the plasma radius.

Computer Simulation of Field Reversal in Mirror Machines

Computer simulation of neutral injection into a mirror machine shows the existence of stable two-dimensional (r, z) field-reversed mirror configurations. The code follows ion orbits in self-consistent magnetic fields; all electron currents have been ignored. For small systems only a few gyroradii in extent, it is only necessary to focus the neutral beam of axis. Stability to the Alfven ion cyclotron mode is due in part to finite-length effects. Some steady states for large systems have also been observed.

Properties of Electrostatic Ion-Cyclotron Waves in a Mirror Machine

Frequency and wavelength of electrostatic ion-cyclotron waves have been measured in a mirror machine. The dominant frequency occurs near the ion-cyclotron fundamental with width ..delta..f/f < 0.02. For most of the plasma buildup and decay the perpendicular wave numbers are consistent with an ion-diamagnetic drift wave ..omega../sub i/* = k/sub perpendicular( c Ei-italic//cB)(1/n) dn/dx at the ion-cyclotron frequency. With increasing wave amplitude the wave spectral properties do not change but an increase in ion energy diffusion is observed, supporting a wave-particle saturation of the mode.

Quasi-linear transport model for mirror machines

A quasi-linear model to describe the evolution of a mirror plasma is presented. It is shown that, as in the 2XIIB mirror experiment, a plasma stream sufficiently reduces rf turbulence so that a high density steady state mirror plasma can be sustained by a neutral beam. The scaling law for this plasma configuration is derived. The energy lifetime is found to be the Spitzer electron-ion drag time even when electron thermal conduction to the external plasma can be neglected.

Electron stabilization of drift-cone modes

The mechanism of electron trapping in E×B guiding center motion is proposed as the mechanism for absolute stabilization of drift-cone modes in mirror geometry. The calculated amplitudes are shown to be in reasonable agreement with experimental results in present mirror machines.

End-loss processes from mirror machines

The processes leading to end loss of ions from a mirror machine are reviewed. These include breakdown of adiabaticity, scattering and energy drag by classical collisions, and scattering by unstable fluctuations. Described are the linear theory of those modes thought to be of significance in present and reactor-size plasmas, and those features known of their nonlinear saturation.

Some preliminary Q calculations for toroidally linked mirror reactors

A computational study has been made of the energy amplification factor Q to be expected in a toroidally linked mirror (TLM) reactor, using the one-dimensional multi-species Fokker-Planck code ISOTIONS. Because of the uncertainty which exists over the effect of ambipolar electric fields on diffusional losses from TLM systems, two model loss terms have been considered. For each model, Q has been calculated for a range of values of the mirror ratio, the ion injection energy ϵinj, and the ‘critical energy’ ϵc, of TLM diffusion theory. For values of ϵc/ϵinj ∼ 0.5, Q is very significantly enhanced with respect to the value in a single mirror machine, even in the relatively pessimistic model.

Experimental determination of the diffusion rate in a mirror machine by means of trapped particle echoes

Echoes associated with the bounce motion of ions are observed in a mirror fusion device. The echoes are initiated by means of two sucessive perturbations of the confining magnetic field. The characteristic time for echo cancellation under diffusion in velocity space is measured. This time is somewhat less than the predicted classical time for Coulomb collisions. The discrepancy may be accounted for either by rf turbulent fields at ωci or by impurities both of which provide an enhancement of the diffusion coefficient.

Supersonic-subsonic flow transition and shock formation and propagation in a dense plasma beam

The axial flow of a supersonic high density plasma beam into an asymmetric mirror machine has been investigated experimentally. It has been found that in front of the second mirror peak, two supersonic‐subsonic flow transitions and shock formations occur. The subsequent motion upstream, of the first and stronger shock front has been measured by the time‐of‐flight method through diamagnetic loop and electric double probe signals. The shock front speed has been found to be one third the speed of sound in the neighborhood of the sonic transition and decreases to zero ahead of the upstream mirror.

High-β, Gas-Stabilized, Mirror-Confined Plasma

A neutral-beam-sustained plasma in the 2XIIB mirror machine is stabilized by hydrogen gas ionized at one mirror. Peak plasma energy densities that exceed the energy density of the vacuum field (beta-circumflexequivalent8n/sub D/E-bar/sub D//B/sub vac//sup 2/approximately-greater-than1) are achieved with deuterons of average energy E-bar/sub D/approx. =9 keV, peak density n/sub D/approx. =1.5 x 10/sup 14/ cm/sup -3/, in a magnetic field B/sub vac/=0.56 T. These high ..beta..'s are sustained for the duration of gas and neutral-beam injection, with no evidence of a ..beta.. limit. (AIP)

Warm plasma stabilization of drift-cone mode at finite beta

The fraction of warm plasma needed to stabilize the drift cyclotron loss-cone mode in a mirror machine is computed. With warm plasma present, a remnant short wavelength instability persists.

Fusion Research (III): New Interest in Fusion-Assisted Breeders

The hybrid reactor employing fusion-fission reactions is discussed from technological and economic viewpoints. The hybrid concept as used with mirror machines and tokamaks is reviewed. Some advantages and disadvantages of using the hybrid system for breeding fissionable fuels are given. (MOW)

Plasma heating in multiple-resonance excitation of a plasma in a mirror machine

By applying 1 kW of microwave power at 2.45 GHz and 1 kW of r.f. power in the frequency range of 4-25 MHz at one end of a mirror machine, where neutral hydrogen gas is injected in a pulsed mode, a plasma density of 2*1011 cm-3 has been generated with an electron temperature of 60 eV and ion temperature of 40 eV. The ion heating mechanism is, principally, collisional thermalization of the applied r.f. power, via coupling to and excitation of the low frequency resonances of the plasma column, in agreement with the theoretical prediction for the case of high total effective collision frequency for momentum transfer for the electrons.