Bohm Value Research Articles

3D simulations of turbulent mixing in a simplified slab-divertor geometry

Three-dimensional simulations of plasma turbulence have been run using the STORM module of BOUT + + in a simple slab geometry aimed at representing a single, isolated tokamak divertor leg. Turbulence is driven primarily by the Kelvin-Helmholtz mechanism due to the sheared ExB flow that forms around the separatrix due to strong radial gradients in the sheath potential which arise from strong radial gradients in the electron temperature. The turbulence forms a mixing layer around the separatrix which spreads heat and particles into the private-flux region. The resulting spread of the electron heat flux is within the experimental range measured on MAST. An effective thermal transport coefficient which is approximately 10% of the Bohm value is measured from the simulations. When a transport coefficient of this magnitude is used in a diffusive axisymmetric simulation, the time-averaged radial profiles share similar features to the full turbulence simulation.

NONLINEAR DYNAMICS OF ACOUSTIC INSTABILITY IN A COSMIC RAY SHOCK PRECURSOR AND ITS IMPACT ON PARTICLE ACCELERATION

An acoustic instability of a shock precursor driven by the pressure gradient of accelerated particles is studied in the nonlinear regime. The nonlinearity steepens unstable acoustic waves and turns them into shocks. The shocks form a shocktrain but they may merge into each other. Traveling wave solutions are obtained analytically in two different cases. In the first case, only acoustic instability is included and the characteristic scale (distance between the shocks) is limited only by the system size (while shocks merge). In the second case, the instability develops out of cyclotron unstable seed magnetohydrodynamic (MHD) waves. The spatial distance between the MHD wave packets sets the scale of the acoustic shocktrain. The internal structure of the individual shocks is presumably determined by the ion skin depth c/ω pi and by the relaxation length of slightly superthermal particle distributions near these shocks. The shocks are assumed to be arbitrarily thin compared with the distance between them which is ensured by a small viscous term. Both types of solutions are dynamically verified by numerical calculations. The hydromagnetic flow in the shock precursor emerging from the acoustic instability is crucial for two recently suggested phenomena in diffusive shock acceleration. One phenomenon is the enhancement of the acceleration rate well above its standard (Bohm) value due to the narrowing of the shock precursor. The second phenomenon is the amplification of the long-scale magnetic field by an inverse cascade of Alfven waves generated by accelerated particles and scattered in k-space on the acoustic perturbations.

Numerical simulations for cold layer formation in an inverse Z-pinch magnetized target fusion system

One-dimensional magnetohydrodynamic simulations have been performed to study cold layer formation in a magnetized target fusion system with an inverse Z-pinch target plasma. Three phases of cold layer evolution has been identified. During the early compression phase, when liner velocities were not high, formation of a “classical” cold layer is observed, with monotonically increasing plasma densities and decreasing temperatures as the liner is approached. During the main compression phase, lasting until close to peak compression, magnetic flux leakage from the plasma to the liner is not important. The cold layer is then characterized by monotonically decreasing plasma temperature, density, and thermal conductivity. This has practical significance, since it would tend to reduce thermal losses to the liner. During the late compression and burn phases, magnetic flux leakage into the liner becomes important. This phase is characterized by a rapid increase in density and a rapid decrease in magnetic field and temperature toward the liner. This yields significantly higher values of thermal conductivity than in the bulk plasma, leading to enhanced thermal losses. During the first two phases, the entire plasma is magnetically confined. During the last phase, the cold layer changes to a wall-confined mode, while the bulk plasma continues to be magnetically confined. This is a major difference from earlier assumptions about wall confinement of such plasmas. These results show that the Kadomtsev stability parameter exceeds unity in the cold layer during the second and third phases, which may be an indication of instability. The choice of the transport model has a significant effect upon plasma evolution and the plasma lifetime. Classical transport yields plasma density levels near the liner that are significantly higher, sometimes by orders of magnitude, than those yielded by Bohm transport. During the main compression phase, Bohm diffusivity yields a lower lifetime, as expected. During the early compression phase, however, the classical lifetime is unexpectedly below the Bohm value. A physical explanation has been provided for these trends.

Observational constraints on energetic particle diffusion in young supernovae remnants: amplified magnetic field and maximum energy

Constraints on the diffusion and acceleration parameters in five young supernova remnants (SNRs) are derived from the observed thickness of their X-ray rims, as limited by the synchrotron losses of the highest energy electrons, assuming uniform and isotropic turbulence. From a joint study of the electrons diffusion and advection in the downstream medium of the shock, it is shown that the magnetic field must be amplified up to values between 250 and 500 µG in the case of Cas A, Kepler, and Tycho, or ∼100 µ Gi n the case of SN 1006 and G347.3-0.5. The diffusion coefficient at the highest electron energy can also be derived from the data, by relating the X-ray energy cutoff to the acceleration timescale. Values typically between 1 and 10 times the Bohm diffusion coefficient are found to be required. We also find interesting constraints on the energy dependence of the diffusion coefficient, by requiring that the diffusion coefficient at the maximum proton energy be not smaller than the Bohm value in the amplified field. This favours diffusion regime between the Kraichnan and the Bohm regime, and rejects turbulence spectrum indices larger than � 3/2. Finally, the maximum energy of the accelerated particles is found to lay between 10 13 and 5 × 10 13 eV for electrons, and around Z × 8 × 10 14 eV at most for nuclei (or ∼2.5 times less if a Bohm diffusion regime is assumed), roughly independently of the compression ratio assumed at the shock. Even by taking advantage of the uncertainties on the measured parameters, it appears very difficult for the considered SNRs in their current stage of evolution to produce protons up to the knee of the cosmic-ray spectrum, at ∼3 × 10 15 eV, and essentially impossible to accelerate Fe nuclei up to either the ankle at ∼3 × 10 18 eV or the second knee at ∼5 × 10 17 eV.

Electron cross-field transport in a miniaturized cylindrical Hall thruster

Conventional annular Hall thrusters become inefficient when scaled to low power. Cylindrical Hall thrusters, which have lower surface-to-volume ratio, are more promising for scaling down. They presently exhibit performance comparable with conventional annular Hall thrusters. The present paper gives a review of the experimental and numerical investigations of electron cross-field transport in the 2.6-cm miniaturized cylindrical Hall thruster (100-W power level). We show that, in order to explain the discharge current observed for the typical operating conditions, the electron anomalous collision frequency /spl nu//sub B/ has to be on the order of the Bohm value, /spl nu//sub B/ /spl ap/ /spl omega//sub c//16. The contribution of electron-wall collisions to cross-field transport is found to be insignificant. The optimal regimes of thruster operation at low background pressure (below 10/sup -5/ torr) in the vacuum tank appear to be different from those at higher pressure (/spl sim/10/sup -4/ torr).

Electron cross-field transport in a low power cylindrical Hall thruster

Conventional annular Hall thrusters become inefficient when scaled to low power. Cylindrical Hall thrusters, which have lower surface-to-volume ratio, are therefore more promising for scaling down. They presently exhibit performance comparable with conventional annular Hall thrusters. Electron cross-field transport in a 2.6 cm miniaturized cylindrical Hall thruster (100 W power level) has been studied through the analysis of experimental data and Monte Carlo simulations of electron dynamics in the thruster channel. The numerical model takes into account elastic and inelastic electron collisions with atoms, electron-wall collisions, including secondary electron emission, and Bohm diffusion. It is shown that in order to explain the observed discharge current, the electron anomalous collision frequency νB has to be on the order of the Bohm value, νB≈ωc/16. The contribution of electron-wall collisions to cross-field transport is found to be insignificant.

Study of particle behaviour at the edge in HT-7 tokamak

The cross-field diffusion coefficient (D⊥) at the edge in the HT-7 tokamak is close to the Bohm value when the line average electron density ranges from 1.5×1019 to 3.0×1019m−3. The energy profile of the particles is derived directly from the Hα(Dα) line shape; the dissociative excitation of molecules is dominating when the local electron temperature is above 10eV. By means of the Monte Carlo method the Dα line shape is also simulated. We find that the molecular dissociation contributes to 57% of neutral atoms and 53% of emission intensity in front of the limiter and 85% of neutral atoms and 82% of emission intensity in front of the wall. The influence of atomic and molecular processes on the energy balance is discussed for the scrape-off layer (SOL) and the power loss from molecular dissociation is found to be 6×104kW at the SOL. The ion Bernstein wave (IBW) can effectively suppress the magnetohydrodynamic behaviour, the fluctuation levels and the turbulence; the D⊥ in front of the limiter declines from 0.84 to 0.2m2.s−1 and the particle confinement time rises from 9 to 12ms.

Instability Driven by Sheath Boundary Conditions and Limited to Divertor Legs

AbstractAn instability driven by electron temperature gradient in combination with sheath boundary condition at the divertor plate is considered. A mode localized between the divertor plate and the X point is found. The further propagation of the mode is terminated by a strong shear near the X point. “Heuristic” boundary condition at the control surface situated somewhat below the X point is suggested. The mode manifests a strong dependence on the radial tilt of the divertor plate, thereby providing some degree of control over the plasma transport in the divertor leg. Estimates of the diffusion coefficient show that it may reach the Bohm value. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On drift instabilities in magnetized target fusion devices

Some versions of magnetized target fusion (MTF) devices will be using a high beta plasma, with local beta exceeding 1. Drift instabilities in such a plasma are electromagnetic and are quite different from the analogous instabilities in a low beta plasma. In a collisionless limit they have been analyzed by El Nadi and Rosenbluth [Phys. Fluids 16, 2036 (1973)] who have shown that the cross-field transport coefficients in such a plasma may exceed a Bohm value. On the other hand, high-density plasma in MTF systems is usually strongly collisional in the sense that the drift frequency for the most dangerous large-scale perturbations is smaller than the ion–ion collision frequency, and the particle mean free path is shorter than the parallel wavelength. This regime is studied in the present paper. It is shown that transport coefficients in the MTF plasma are usually smaller than the Bohm diffusion coefficient.

Transport into and across the scrape-off layer in the ASDEX Upgrade divertor tokamak

The elements of transport into and across the scrape-off layer in the poloidal divertor tokamak ASDEX Upgrade are analysed for different operational regimes with emphasis on enhanced confinement regimes with an edge barrier. Utilizing the existing set of edge diagnostics, especially the high-resolution multi-pulse edge Thomson scattering system, in combination with long discharge plateaus, radial sweeps and advanced averaging techniques, detailed radial mid-plane profiles of diverted plasmas are obtained. Profiles are smooth across the separatrix, indicating strong radial correlation, and there is no remarkable variation across the second separatrix either. Together with measured input, recycling, pumping and bypass fluxes, a corrected separatrix position is determined and transport characteristics are derived in the different radial zones generally identified in the profile structure. Transport in the steep gradient region inside and across the separatrix shows typical ballooning-type critical electron pressure gradient scaling and, in parallel, even a clear correlation between radial electron density and temperature decay lengths (e.g. ηe = d(ln T)/d(ln n)~2 for type-I ELMy H-modes). These findings indicate the importance of stiff profiles in this region, while diffusion coefficients are secondary parameters, determined essentially by the source distribution. The outer scrape-off layer wing exhibits a more filamentary structure with preferential outward drift especially in high-performance discharges, with formal diffusion coefficients far above the Bohm value in agreement with results on the old ASDEX experiment. A basic mechanism involved there seems to be partial loss of equilibrium and fast curvature-driven outward acceleration, in principle well known from theory, investigated decades ago in pinch experiments and utilized recently in high-field-side pellet fuelling.

Calculation of transport parameters in KT-1 tokamak edge plasma

Abstract The radial profiles of KT-1 tokamak (major radius of 27 cm, minor radius of 4.25 cm, two poloidal stainless-steel limiters) edge plasma parameters are measured using single and triple electric probes. The particle transport parameters are calculated from the measured edge plasma parameters, and the results are analyzed by the simple fluid approximations. The cross-field particle diffusion coefficient ( D ⊥ ) in the boundary plasma of the KT-1 is calculated from the density scrape-off length ( λ n ) measured by using a triple probe. The particle density and electron temperature fall exponentially in the radial direction with the e-folding length of λ n =0.13 cm and λ e =0.41 cm, respectively. From the scrape-off layer (SOL) model, the experimental values of scrape-off length ( λ n ) is used to calculate the cross-field diffusion coefficient ( D ⊥ =1.2×10 3 cm 2 /s), roughly corresponding to one third of the typical Bohm value. A simple SOL model with the contribution of recombination is introduced to evaluate the Bohm diffusion in the KT-1 tokamak edge plasma. Cross-field heat conductivity calculated from these deduced values is ∼5.2 D ⊥ in the SOL of KT-1 edge plasma. These results provide the finally certain information for edge particle transport in the KT-1 boundary plasmas.

Magnetic Field Line Wandering and Shock‐Front Acceleration: Application to the Radio Emission of SN 1987A

The superposition of random fluctuations δ on a main, regular magnetic field 0 has been shown by Ragot to produce, on the scales of interest, a nondiffusive random walk of the magnetic field lines in the quasi-linear regime of turbulence. The spreading Δx2 of the field lines across the direction of 0 increases as zβ, z being the distance along 0 with a transport exponent β that is not necessarily equal to 1. This puts into question the diffusivity of magnetic field lines in a non-quasi-linear regime as well and could imply an anomalous transport of the cosmic rays accelerated at a shock front if their decorrelation time from the field lines is longer than their acceleration time. Under the assumption of such a long decorrelation time, the acceleration time of cosmic rays scattered along the wandering field lines is derived here as a function of the obliquity and speed of the shock for a general transport exponent of the field lines. It is shown that for high-speed shocks, the importance of magnetic field line wandering (MFLW) is not limited to quasi-perpendicular shocks as usually believed. Moreover, the turbulence ahead of the shock is in a non-quasi-linear regime on the length scale traveled by accelerated particles whenever MFLW is important. The inclusion of MFLW can make the acceleration time depart by orders of magnitude from its value estimated in the approximation of simple scattering. This discrepancy is actually most welcome to explain the acceleration time of GeV electrons at the reappearance of SN 1987A in the radio waveband, since the inferred diffusion coefficient along the shock normal is about 5 orders of magnitude greater than the limiting Bohm value of a cross-field scattering coefficient. From the requirement of a realistic turbulence spectrum and in the approximation of quasi-linear transport coefficients, it is found that the magnetic field lines ahead of the SN 1987A shock strongly supradiffuse (β ≈ 1.8) and that the compression ratio of the shock is larger than 3. Finally, this paper argues in favor of a radio silence of SN 1987A prior to 1990 due to a lack of scattering of the GeV electrons when the shock speed exceeds about one-tenth of the speed of light.

Anomalous electron mobility in a coaxial Hall discharge plasma.

A comprehensive analysis of measurements supporting the presence of anomalous cross-field electron mobility in Hall plasma accelerators is presented. Nonintrusive laser-induced fluorescence measurements of neutral xenon and ionized xenon velocities, and various electrostatic probe diagnostic measurements are used to locally determine the effective electron Hall parameter inside the accelerator channel. These values are then compared to the classical (collision-driven) Hall parameters expected for a quiescent magnetized plasma. The results indicate that in the vicinity of the anode, where there are fewer plasma instabilities, the electron-transport mechanism is likely elastic collisions with the background neutral xenon. However, we find that in the vicinity of the discharge channel exit, where the magnetic field is the strongest and where there are intense fluctuations in the plasma properties, the inferred Hall parameter departs from the classical value, and is close to the Bohm value of (omega(ce)tau)(eff) approximately 16. These results are used to support a simple model for the Hall parameter that is based on the scalar addition of the electron collision frequencies (elastic collision induced plus fluctuation induced), as proposed by Boeuf and Garrigues [J. Appl. Phys. 84, 3541 (1998)]. The results also draw attention to the possible role of fluctuations in enhancing electron transport in regions where the electrons are highly magnetized.

Diffusive acceleration of electrons in SN 1987A

We suggest that synchrotron radiation emitted by electrons undergoing diffusive acceleration at the supernova blast wave is the cause of the reappearance of radio emission from SN 1987A in 1990 July. Making reasonable assumptions concerning adiabatic losses and the magnetic field in the preexplosion stellar wind, we find the light curve and spectrum which would be produced by a constant rate of particle injection occurring in a localized region of the shock front; i.e., in a clump or knot. Observations indicate that two such clumps have been encountered to date. From the observed delay in the switch-on of the emission between 843 MHz and 4.8 GHz we find a spatial diffusion coefficient for electrons of κ<SUB>normal</SUB>_ = 2 x 10^20^ m^2^ s^-1^. This value agrees with that found for the second clump and is substantially greater than the Bohm value. Estimating the magnetic field to be 10^-7 T and assuming the diffusion coefficient is constant leads to the conclusion that the shock encountered the first clump on about day 900 and the second clump on day 1190. From the observed spectrum we find the compression ratio of the shock responsible for electron acceleration to be ~2.7. This implies strong modification of the shock front which may be due to the acceleration of cosmic rays.

Observation of a current-limited double layer in a linear turbulent-heating device

Time- and space-resolved measurements of strong double layers (DLs) have been carried out for the first time on a linear turbulent-heating device, together with those of fluctuation spectra and precise current measurements. A stable stong DL is formed even when the electric current through the DL is less than the so-called Bohm value. Discussion of the formation and decay processes is given, indicating a transition from an ion-acoustic DL to a monotonic DL.

Observations of Anomalous Plasma Transport Produced by Magnetic Field Errors

The plasma transport to the internal ring of a multipolelike device was increased by over an order of magnitude by the addition of a 1% magnetic field error which causes field lines to spiral across the confinement region. Magnetic field perturbations which keep the field lines closed produce a negligible increase in plasma loss to the internal ring. The plasma is observed to flow radially toward the loop at the region of the perturbation and then E × B drifts azimuthally affecting the density profile everywhere in the device. The increased loss under the influence of a 1% perturbation corresponds to an effective diffusion coefficient that is ≃20% of the Bohm value. Detailed experimental studies of the plasma transport and azimuthal density profiles are in qualitative agreement with a model which considers diffusion of plasma along the perturbed magnetic field to the internal ring.

Plasma Containment in a Quadrupole Configuration

The containment times of afterglow plasmas in hydrogen, helium, and neon were measured in a linear quadrupole machine (LM-1), where ne ≲ 2 × 1012, Te ≲ 10 eV, Ti &amp;lt; 1 eV, mean free path λ ≲ 100 cm, connection length ≈ 20 cm, and electron-ion collision time ≈ 10−7 sec. Particle collectors showed the losses to be mainly radial. The plasmas in the ∮ dl/B stable region decayed in times of order a millisecond (about 10 times the Bohm value) which increased with IQ) the conductor current, to a roughly constant value, and decreased as Te increased. An axial magnetic field which introduced shear (θ ≥ 1/30 rad/cm for the main plasma) caused negligible change to the containment time in helium, with a slight improvement in neon. Various instabilities were observed. Pronounced variations in probe signals and plasma loss rates at different axial positions suggested a convective structure which persisted in the afterglow for some milliseconds. The origin of the radial loss inside the stable region may be due to a low-frequency flutelike mode or possibly to the convective structure in the plasma.

Collisional Drift Waves—Identification, Stabilization, and Enhanced Plasma Transport

Density-gradient-driven collisional drift waves are identified by the dependences of ω and k on density, temperature, magnetic field, and ion mass, and by comparisons with a linear theory which includes resistivity and viscosity. Abrupt stabilization of azimuthal modes is observed when the stabilizing ion diffusion over the transverse wavelength due to the combined effects of ion Larmor radius and ion-ion collisions (viscosity) balances the destabilizing electron-fluid expansion over the parallel wavelength, determined by electron-ion collisions (resistivity). The finite-amplitude (ũ/n0 ≃ 10%) coherent oscillation, involving the entire plasma body, shows a phase difference between density and potential waves (which is predicted by linear theory for growing perturbations). The wave-induced radial transport exceeds classical diffusion, but is below the Bohm value by an order of magnitude. Although observations have been extended to magnetic fields three times those for drift-wave onset, turbulence has not been encountered.

Confinement of Injected Plasmas in Stellarators

Plasmas produced by a washer plasma gun have been injected into B-3, which is a twisted figure-eight stellarator, and Etude, which is a racetrack stellarator. Both have l = 3 helical windings. In the injected plasmas ne ≤ 5 &amp;lt; 109, Te ≈ 5-8 eV, and Ti is probably greater than Te. The mean free paths for electron collisions were in the range 10-100 machine lengths. The observed confinement times varied with confining field as Bm with 0.6 &amp;lt; m &amp;lt; 1.2 for B ≤ 20 kG in B-3. In Etude, the confinement times varied from the Bohm value at zero rotational transform ι and increased by a factor 20 when ι = 5.43 rad. In B-3 the confinement times varied from about twice the Bohm value when only the geometric transform was present and increased by a factor 30 when ι was increased to 19 rad. It was not possible to decide if the increase of confinement time was due to effects of shear or rotational transform.