Compact Toroid Research Articles

Magnetic flux trapping during field reversal in the formation of a field-reversed configuration

The flow of plasma and magnetic flux toward a wall is examined in a slab geometry where the magnetic field is parallel to the wall. Magnetohydrodynamic (MHD) flow with a quasisteady approximation is assumed that reduces the problem to three coupled ordinary differential equations. The calculated behavior shows that a thin current sheath is established at the wall in which a variety of phenomena appear, including significant resistive heating and rapid deceleration of the plasma flow. The sheath physics determines the speed at which flux and plasma flow toward the wall. The model has been applied to the field-reversal phase of a field-reversed theta pinch, during which the reduced magnetic field near the wall drives an outward flow of plasma and magnetic flux. The analysis leads to approximate expressions for the instantaneous flow speed, the loss of magnetic flux during the field reversal phase, the integrated heat flow to the wall, and the highest possible magnetic flux retained after reversal. Predictions from this model are compared with previous time-dependent MHD calculations and with experimental results from the TRX-1 [Proceedings of the 4th Symposium on the Physics and Technology of Compact Toroids, 27–29 October 1981 (Lawrence Livermore National Laboratory, Livermore, CA, 1982), p. 61] and TRX-2 [Proceedings of the 6th U.S. Symposium on Compact Toroid Research, 20–23 February, 1984 (Princeton Plasma Physics Laboratory, Princeton, NJ, 1984), p. 154] experiments.

Adiabatic compression and interchange stability of rotating compact toroid plasmas

The adiabatic compression of plasmas with mass rotation is formulated as a variational principle based on some constants of the motion. A numerical code is constructed and Grad’s alternating dimensions method is used. The calculations simulate compression either by increasing the flux outside the plasma or by liner compression. Changes in Mach number and some stability criteria during compression are monitored. Interestingly, the Mach number remains almost constant despite a spin up of the plasma. An extension of the interchange stability criterion for rotating plasmas is developed. Interchange stable equilibria exhibit very high current density near the separatrix and tend to be more elongated. Interchange instability offers a mechanism to generate rotation throughout the plasma.

Influence of embedding media on DNA structure in herpes simplex virus type 1

The organization of encapsidated herpes simplex viral DNA in situ was examined by use of the osmium-amine stain specific for DNA. After either formaldehyde or glutaraldehyde fixation the DNA is packaged in a compact toroid without inner structure with Epon or GMA embedment but revealed a complex inner structure with Lowicryl K4M embedment. In the latter there was an inner cylindrical core, 50 X 80 nm, around which were apposed one or more thick filaments of 5-8 nm diameter. Thinner DNA filaments of 3-4 nm diameter form a cage of loose coils around the core with an intervening space of approximately 15 nm. Lowicryl embedding may be considered as a tool to investigate the packaging of viral DNA in virions.

Compact toroid created by rotating relativistic electron beams

A hollow, rotating relativistic electron beam with ν/γ≫1 may be stably propagated inside an initially field-free, closed metal tube containing neutral hydrogen at a pressure of about 100 mTorr. Under these circumstances the beam is charge neutralized but not current neutralized, and propagates at an equilibrium radius determined by the pressure balance of the self-magnetic fields inside and outside the beam. The axial component of the magnetic field is in opposite directions inside and outside the beam, the total flux inside the tube being zero. During its passage the beam ionizes and heats the neutral gas such that when the beam pulse ends, the magnetic field of the beam is ‘‘frozen’’ into the resulting plasma. The plasma confinement configuration generated by a single beam is a reversed-field linear pinch with an axial current which returns through the wall of the tube. To produce a completely closed plasma configuration, a second rotating electron beam is injected from the opposite end of the chamber between the first beam and the wall. It is possible by this means to bring the persistent axial current to zero, but only under rather restricted conditions because the propagation of the second beam is adversely affected by the peripheral plasma produced by the first beam. However, the principal of this novel method of producing a magnetically confined plasma was effectively demonstrated.

Investigations of the magnetic structure and the decay of a plasma-gun-generated compact torus

The results of a series of experimental measurements of compact toroidal (CT) plasmas produced by a magnetized coaxial plasma gun injecting into a flux-conserving metallic liner are reported. The experiments were performed on the Beta II facility at Lawrence Livermore National Laboratory. The magnetic equilibria are well described by a force-free eigenmode structure that results from an extension of Taylor’s theory of the reversed-field pinch. Consideration of helicity conservation during relaxation of the composite plasma-gun flux-conserver system to the final state equilibrium yields theoretical expressions that are compared with the experiment. In particular the CT poloidal flux (ψpol) and the overall electrical efficiency for producing the CT are predicted to be functions of the plasma gun inner-electrode flux (ψgun) and the volt-seconds input to the gun discharge (∫∞0 V dt). Away from a cutoff at too low values of ∫∞0 V dt or too high values, ψgun ,ψpol scales linearly with the square root of the product of ψgun and ∫∞0 V dt, whereas the electrical efficiency equals about 13% for ∫∞0 V dt/ψgun ≊10. For an electrical energy input Win =45 kJ, CT’s are produced with poloidal plus toroidal field energy up to WB =8 kJ and toroidal plasma current Itor =330 kA. The chord-averaged plasma density is 2–4×1014 cm−3, and the plasma volume equals 150 liters. The radius of the flux conserver is 37.5 cm, and the axial length is 40 cm. If a bias flux ψb is superimposed on the flux conserver, n=1 tilting is observed when ψb/ψpol exceeds a ratio of about 0.20 to 0.25. Impurity radiation measured by a pyroelectric detector accounts for all of the plasma magnetic energy if uniform volume emission of radiation is assumed. The dominant impurities observed are carbon and oxygen. Helium-like lines are not observed, indicating that the plasma has not ‘‘burned through’’ the low electron temperature radiation maxima. The experimentally observed decay times (defined by the e-folding time of plasma magnetic fields) are 80 to 160 μsec—consistent with Zeff =2 and Te in the range 5–10 eV if classical resistivity is assumed. A zero-dimensional rate equation model of impurity radiation loss gives a reasonably good account of the experimental observations and predicts that the carbon concentration must be reduced to the level of a few percent to allow burnthrough of the low-Te carbon radiation barrier. Glow discharge cleaning of the gun electrodes and flux conserver resulted in a 20% increase of the e-folding time of plasma magnetic fields (from an average value 115 to 140 μsec). The CT plasma density was observed to scale linearly with the electrical energy input to the gun discharge and to be only weakly dependent on the filling pressure and timing of pulsed deuterium gas valves. It seems likely that further improvements in increasing plasma lifetime can be made by improving the vacuum conditions and discharge cleaning methods and experimenting with the gun electrode materials.

Magnetohydrodynamic Equilibrium with Spheroidal Plasma-Vacuum Interface –Compact Toroid without Toroidal Magnetic Field–

The Grad-Shafranov equations for an oblate and a prolate spheroidal plasmas are solved analytically under the assumptions, B ϕ =0 and d p /dψ=constant. Here B ϕ is the toroidal magnetic field, p is the kinetic pressure, and ψ is the magnetic flux function. The plasmas in magnetohydrodynamic equilibrium are shown to be toroidal . The equilibrium magnetic-field configurations outside the spheroidal plasmas are considerably different from that of a spherical plasma. A line cusp or two point cusps appear outside the oblate or the prolate spheroidal plasma, respectively.

Suppression of the n=2 rotational instability in field-reversed configurations

Compact toroid plasmas formed in field-reversed theta pinches are generally destroyed after 30–50 μsec by a rotating n=2 instability. In the reported experiment, instability is controlled, and the plasma destruction is avoided in the TRX-1 theta pinch through the application of octopole magnetic fields. The decay times for loss of poloidal flux and particles are unaffected by the octopole fields. These decay times are about 100 μsec based on inferences from interferometry and excluded flux measurements. The weak, rotating elliptical disturbance (controlled n=2 mode) also made possible a novel determination of the density profile near the separatrix using single-chord interferometry. The local density gradient scale length in this region is found to be about one ion gyrodiameter.

Review of the Fifth Symposium on the Physics and Technology of Compact Toroids, Bellevue, Washington, November 16–18, 1982

Review of the Fifth Symposium on the Physics and Technology of Compact Toroids, Bellevue, Washington, November 16–18, 1982

Compact toroid experiments: Spheromaks and field-reversed configurations

Compact toroids (CT) containing both poloidal and toroidal magnetic field, spheromaks, are generated in the CTX experiment using a magnetized coaxial plasma gun, and are trapped and stably confined in an oblate flux conserver. Total configuration lifetimes are observed up to ∼ 0.8 ms, consistent with classical resistive decay. The field reversed configuration (FRC) is a high beta, axisymmetric, highly prolate compact toroid, containing only poloidal magnetic field, formed in a field-reversed theta pinch. A quiescent confinement period of 30 to 90 μs with T i ∼ 200–500 eV and n ∼ 5 × 10 15 cm −3 is terminated by an n = 2 rotational instability. The FRC is stable to MHD modes including the tilting instability.

Magnetohydrodynamic and double adiabatic stability of compact toroid plasmas

The linear stability of compact toroids is examined in the magnetohydrodynamic and double adiabatic models. The long-thin approximation in ideal magnetohydrodynamics is used to investigate tilting and shifting modes in field reversed configurations without toroidal fields. A necessary and sufficient condition is obtained and used to show that the combination of flux surface shaping and profile flatness results in stability to a class of transverse modes in a region about the O point. The double adiabatic model yields for general confined plasmas a sufficient condition for stability in the form of six ordinary differential equations along each field line. Further reduction of the condition to a single second-order equation depends on the sign of ∂S/∂B, where S(ψ,B)=p∥B5/p3⊥ is a combination of the two entropies. Strong stabilizing effects of pressure anisotropy are shown.

Report on the Fourth Symposium on the Physics and Technology of Compact Toroids, Livermore, California, October 27-29, 1981

Report on the Fourth Symposium on the Physics and Technology of Compact Toroids, Livermore, California, October 27-29, 1981

Analytic model of the radiation-dominated decay of a compact toroid

A simple analytic model of the radiation-dominated decay of a compact torus is presented. Several striking features of various experiments (finite lifetime, linear current decay, and insensitivity of the lifetime to density or stored magnetic energy) are explained by the model. A simple criterion is given for the maximum tolerable impurity density.

Stability and Confinement of Spheromaks and Field Reversed Configurations

The formation, confinement and stability of two types of compact toroids, spheromaks and field reversed configurations (FRC), are reviewed. Spheromaks, which contain both toroidal and poloidal magnetic fields, have been formed with magnetized coaxial plasma guns, by a combination of Z- and θ-pinch techniques and by an electrodeless slow induction technique, and trapped in both prolate and oblate flux conservers. As predicted by theory, the prolate configuration is unstable to the tilt mode, but the oblate configuration with a conducting wall is stable. Configuration lifetimes of up to 0.8 ms are observed. The FRC is a high-beta, highly prolate compact toroid formed with field-reversed theta-pinch techniques and having purely poloidal magnetic field. Theory predicts unstable fluting and internal tilting modes, but they are not observed experimentally. Configurations with high densities ∼ 1015 cm-3 and with lifetimes of 50–120 μs are terminated by an n = 2 rotational mode of instability.

Field-reversed experiments (FRX) on compact toroids

Equilibrium, stability, and confinement properties of compact toroids produced in field-reversed theta-pinch experiments (FRX) are reported. Two experimental facilities, FRX-A and FRX-B, have been used to study highly elongated compact toroid plasmas confined in a purely poloidal field geometry. Spatial scans and fill pressure scaling of the equilibrium plasma parameters are presented. Plasma conditions range from Te∼150 eV, Ti∼800 eV, nm∼1×1015 cm−3 to Te∼100 eV, Ti∼150 eV, nm∼4×1015 cm−3. Typical confined plasma dimensions are: major radius R∼4 cm, minor radius a∼2 cm, and total length 35–50 cm. The plasma configuration remains in a stable equilibrium for up to 50 μsec followed by the destructive n = 2 rotational instability. The stable period prior to the onset of the rotational mode is up to one hundred times greater than characteristic Alfvén transit times of the plasma. This stable period increases and the mode growth rate decreases with increased a/ρi (where ρi is the ion gyroradius). Agreement of experimental and theoretical mode frequencies for the instability is observed. Preferential particle loss has been proposed as a likely cause of rotation. The particle inventory at the onset of the instability is consistent with this hypothesis. The particle loss rate is also consistent with the predicted anomalous transport near the separatrix. Contributions to rotational instability from diffusion, end-shorting, equipartition, and compression are also discussed.

Finite Larmor radius model for axisymmetric compact toroids

Stability equations for axisymmetric compact toroidal configurations without a toroidal magnetic field are derived in a variational form. The application of a particular ordering procedure gives equations which include the coupling of geometry to finite Larmor radius as well as including resonant ion effects. The equations are readily obtained by applying the ordering assumptions to a variational dispersion functional form of the Vlasov-fluid equations. Application of the dispersion functional to find necessary and sufficient conditions for stability are made for the case of small, but finite Larmor radius and for the case of zero Larmor radius. The mathematical result that the zero Larmor radius case is more optimistic is physically understood in the context of an interesting stabilizing mechanism involving parallel kinetic effects.

Compact Toroidal Plasma with Toroidal and Poloidal Magnetic Fields

Compact toroidal plasma has been experimentally obtained in a drum-type copper vessel on injecting an annular plasma stream from a magnetized plasma gun. Toroidal and poloidal magnetic fields, B t and B p , of the plasma toroid show a typical exponential decay with 110 µs and no MHD instability is observed. Experimental data of B t and B p configuration for long confinement are described fairly well by the model, which is the fundamental-mode state of the minimum energy force-free equilibrium estimated from the low- β limit Grad-Shafranov equation. The configuration of the stable plasma is hence fully-determined by the metal vessel geometry.

Mechanism of Tinting Mode Instability in Compact Toroids

Mechanism of Tinting Mode Instability in Compact Toroids

Motion of a Compact Toroid inside a Cylindrical Flux Conserver

Compact toroids have been generated in a cylindrical resistive flux conserver. They are observed to rotate so that their major axis is perpendicular to the axis of the flux conserver. Subsequently they remain stationary and their magnetic fields decay with a time constant of about 100 \ensuremath{\mu}s. This is the first observation of the predicted tipping mode and its saturation when no external fields are present. The compact toroids contain toroidal fields and are initially prolate in shape.

A Compact Toroidal Plasma Produced by a Hard Core Theta Pinch with Poloidal Field Coils

A Compact Toroidal Plasma Produced by a Hard Core Theta Pinch with Poloidal Field Coils