Search

International audience; Magnetic cusps have been used for more than 50 years to limit charged particle losses to the walls and confine the plasma in a large variety of plasma sources or ion sources. Quantification of the effective loss area has been the subject of many experimental as well as theoretical investigations in the 1970-1990's. In spite of these efforts there is no fully reliable expression of the effective wall loss as a function of cusp magnetic field, electron temperature, ion mass, gas pressure, etc… We describe in this paper a first attempt at obtaining scaling laws for the effective loss width of magnetic cusps, based on two-dimensional PIC MCC (Particle-In-Cell Monte Carlo Collisions) simulations. The results show that the calculated leak width follows a 1/B scaling in the collisionless low B limit, is approximately proportional to the hybrid gyroradius with an ion velocity equal to the Bohm velocity and is proportional to the square root of gas pressure in the collisional limit.

A one-dimensional hydrodynamic model is developed for a magnetized plasma sheath, consisting of Maxwell electrons, q-non-extensive electrons, and thermal ions. A significant change is observed in the quantities characterizing isolated dust particles in the presence of superextensive electrons (q

Taking into account the dust grain size distribution, the Bohm criterion is revisited by means of a one-dimensional, stationary, and non-magnetized theoretical model. An argon plasma is considered where the electrons are characterized by the Boltzmann distribution; however, the other species are described by the fluid equations. The dust grain charge number is described by the orbit motion limited model and their size is modeled by a Gaussian law. The generalized Bohm criterion has been calculated by using the Sagdeev's pseudo-potential approach. The numerical results show that the Bohm velocity values are greater than those of the classical model where the dust grains are absent, and they exhibit a peak. Moreover, by taking into account the dust size distribution, the obtained Bohm velocity values are practically comparable to those found in the mono-size model for a mean radius of the dust grains. Furthermore, it is found that the presence of mono-energetic electrons increases the Bohm velocity values. The dust grain surface potential at equilibrium is also calculated and discussed.

The magnetic induction equation for an axially symmetric magnetic field reveals an interesting feature, when the Bohm plasma diffusion is incorporated. The 1/B dependence of Bohm diffusion allows the induction equation to transform into a simple heat equation which admits an exact solution when the plasma temperature is constant. When the diffusion velocity satisfies a certain condition, the axially symmetric magnetic field can be significantly enhanced.

Bohm criterion for dust-electron plasmas induced by UV irradiation is investigated by Sagdeev potential, taking into account the self-consistent dust charge variation. In the collisionless limit, the Boltzmann electron distribution and dust cold fluid in the sheath are adopted. It is found that the dust Bohm velocity decreases with increasing dust density in the bulk plasma. The results are examined to be reliable by the quantitative analysis of Sagdeev potential.

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.

Determining the scaling of transport with beta (β), the ratio of the plasma kinetic pressure to the magnetic pressure, helps to differentiate between various proposed theories of turbulent transport since mechanisms that are primarily electrostatic show little change in transport with increasing β, while primarily electromagnetic mechanisms generally have a strong unfavorable β scaling. Experiments on the DIII-D tokamak [J.L. Luxon, Nucl. Fusion 42, 614 (2002)] have measured the β scaling of heat transport with all of the other dimensionless parameters held constant in high confinement mode (H-mode) plasmas with edge localized modes. A four point scan varied β from 30% to 85% of the ideal ballooning stability limit (normalized beta from 1.0 to 2.8) and found no change in the normalized confinement time, i.e., Bτth∝β−0.01±0.09. The measured thermal diffusivities, normalized to the Bohm diffusion coefficient, also did not vary during the β scan to within the experimental uncertainties, whereas the normalize...

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.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.

Experiments and theory on collisional diffusion and viscosity in quiescent single-species plasmas demonstrate enhanced transport in the two-dimensional (2D) bounce-averaged regime, limited by shear in the plasma rotation. For long plasma columns, the measured diffusion agrees quantitatively with recent theories of three-dimensional long-range E×B drift collisions, and is substantially larger than predicted for classical velocity-scattering collisions. For short plasmas, diffusion is observed to be enhanced by Nb, the number of times a thermal particle bounces axially before being separated by shear. Equivalently, recent theory in the 2D bounce-averaged regime shows how diffusion decreases with increasing shear, generalizing the zero-shear perspective which gives Bohm diffusion. Viscosity is similarly enhanced in the 2D regime, but there is presently only qualitative agreement with theory. These results apply to both non-neutral and neutral plasmas, and provide the first rigorous analysis of shear reductio...

A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with low-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the relativistic quasilinear diffusion coefficients are calculated explicitly for magnetically-trapped particle distributions in axisymmetric magnetic geometry in terms of drift-bounce resonant contributions associated with low-frequency fluctuations which conserve the first adiabatic invariant.

The fluid model for positive ions is used together with the assumption of a constant ion mean free path to examine the structure of the plasma-wall sheath at low and medium pressures in plasmas where ionization is by electron impact and the ion temperature is set to zero. It is shown that in the near collisionless regime there is the same structure as was found with the constant collision frequency for momentum transfer model with the Bohm speed playing the same role and similar scaling of the transitional layer. At higher pressures there is again no transitional layer, only plasma joining smoothly to a collisional sheath, thus the Bohm criterion has no significance, but the scaling is with a different exponent than for the mobility case. No fundamental differences are found between the two models. An expression is derived to describe the boundary between the parameter region where the Bohm criterion applies and that where it does not.

A hollow-cathode planar magnetron (HCPM), built by surrounding a planar sputtering-magnetron cathode with a hollow-cathode structure (HCS) [Z. Wang and S. A. Cohen, J. Vac. Sci. Technol. A 17, 77 (1999)], is operable at substantially lower pressures than its planar-magnetron counterpart. HCPM operational parameters depend on the inner diameter D and length L of its cylindrical HCS. Only when L is greater than L0, a critical length, is the HCPM operable in the new low-pressure regime. The critical length varies with HCS inner diameter D. Explanations of the lower operational pressure regime, critical length, and plasma shape are proposed and compared with a one-dimension diffusion model for energetic electron transport. At pressures above 1 mTorr, Bohm diffusion (temperature≅primary electron energy), with an ambipolar constraint, can explain the ion–electron pair creation required to sustain the discharge. At the lowest pressure, ∼0.3 mTorr, collision-limited diffusion creates fewer ion–electron pairs than...

Bohm criterion, originally derived for an isothermal-electron and cold-ion plasma, is often used as a rule of thumb for more general plasmas. Here, we establish a more precise determination of the Bohm criterion that are quantitatively useful for understanding and modeling collisional plasmas that still have collisional mean-free-path much greater than plasma Debye length. Specifically, it is shown that electron heat flux, rather than the isothermal electron assumption, is what sets the Bohm speed to be k B ( T e ∥ + 3 T i ∥ ) / m i with T e , i ∥ the electron and ion parallel temperature at the sheath entrance and mi the ion mass.

This paper presents the behavior of plasma profiles of a sheath in unmagnetized collisionless plasma in the presence of nonextensively distributed two-temperature electrons and isothermal ions. A theoretical model is developed where isothermal ions are described by the conventional hydrodynamic equations along with the effect of electron nonextensivity described by q-distribution function. The plasma sheath parameters like Bohm velocity, potential, and density profiles in the presence of nonextensively distributed two-temperature electrons and isothermal ions are investigated.

Bohm criterion is revisited in the framework of a one-dimensional stationary and unmagnetized low-pressure argon and helium plasma mixture containing non-thermal electrons and dust grains model. Dust grains, electron non-thermality, and ions density ratio effects on Bohm velocities along with dust grain charge number |Φd0|, are investigated. It is revealed that Bohm velocities are highly correlated, with their profiles exhibiting a moving peak. Mixing the two gases allowed the appearance of subsonic (argon) as well as supersonic (helium) Bohm velocities. The present model may be generalized to many ion species plasmas.

The time-dependent solution of diffusion equation by the Fourier integration provides the axial diffusion velocity of a plasma packet, which is a key element of the plasma propagation in a plasma jet operated by the several tens of kHz. The plasma diffusion velocity is higher than the order of un ∼ 10 m/s at a high electric-field region of plasma generation and it is about the order of un ∼ 10 m/s at the plasma column of a low field region in a jet-nozzle inside. Meanwhile, the diffusion velocity is slower than the order of un ∼ 10 m/s in the open-air space where the plasma density flattens due to its radial expansion. Using these diffusion velocity data, the group-velocity of plasma diffusion wave-packet is given by ug ∼ cs2/un, a combination of the diffusion velocity un and the acoustic velocity cs. The experimental results of the plasma propagation can be verified with the plasma propagation in a form of the wave-packet whose propagation velocity is 104 m/s in a tube inside and is as fast as 105 m/s in...

The sheath formation within a low-pressure collisional plasma is analysed by means of a two-fluid model. The Bohm criterion takes into account the effects of the electric field and the inertia of the ions. Numerical results yield that these effects contribute to the space charge formation, only, if the collisionality is lower than a relatively small threshold. It follows that a lower and an upper limit of the drift speed of the ions exist where the effects treated by Bohm can form a sheath. This interval becomes narrower as the collisionality increases and vanishes at the mentioned threshold. Above the threshold, the sheath is mainly created by collisions and the ionisation. Under these conditions, the sheath formation cannot be described by means of Bohm like criteria. In a few references, a so-called upper limit of the Bohm criterion is stated for collisional plasmas where the momentum equation of the ions is taken into account, only. However, the present paper shows that this limit results in an unrealistically steep increase of the space charge density towards the wall, and, therefore, it yields no useful limit of the Bohm velocity.

Experimental observation of the electron density variation in inductively coupled plasmas with the electron energy probability function (EEPFs) was performed at various gas pressures at two RF powers (25 W and 200 W). The measured EEPFs at high power discharges (200 W) showed a Maxwellian distribution, while evolution of the EEPFs from a bi-Maxwellian distribution to a Druyvesteyn-like distribution was observed at low RF powers (25 W) with increasing pressure. A discrepancy of the electron density variation between the two RF powers was observed. This difference is explained by the modified collisional loss and the Bohm velocity from the EEPF of the bi-Maxwellian distribution and the Druyvesteyn–like distribution.

A study on the transport of charged particles across a magnetic filter field has been carried out in a double plasma device (DPD) and presented in this manuscript. The DPD is virtually divided into two parts viz. source and target regions by a transverse magnetic field (TMF) which is constructed by inserting strontium ferrite magnets into two stainless steel rectangular tubes. Plasma electrons are magnetized but ions are unmagnetized inside the TMF region. Negative voltages are applied to the TMF tubes in order to reduce the loss of electrons towards them. Plasma is produced in the source region by filament discharge method and allowed to flow towards the target region through this negatively biased TMF. It is observed that in the target region, plasma density can be increased and electron temperature decreased with the help of negatively biased TMF. This observation is beneficial for negative ion source development. Plasma diffusion across the negatively biased TMF follows Bohm or anomalous diffusion process when negative bias voltage is very less. At higher negative bias, diffusion coefficient starts deviating from the Bohm diffusion value, associated with enhanced plasma flow in the target region.

An electron energy filter (EEF) is embedded in the Large Volume Plasma Device plasma for carrying out studies on excitation of plasma turbulence by a gradient in electron temperature (ETG) described in the paper of Mattoo et al. [S. K. Mattoo et al., Phys. Rev. Lett. 108, 255007 (2012)]. In this paper, we report results on the response of the plasma to the EEF. It is shown that inhomogeneity in the magnetic field of the EEF switches on several physical phenomena resulting in plasma regions with different characteristics, including a plasma region free from energetic electrons, suitable for the study of ETG turbulence. Specifically, we report that localized structures of plasma density, potential, electron temperature, and plasma turbulence are excited in the EEF plasma. It is shown that structures of electron temperature and potential are created due to energy dependence of the electron transport in the filter region. On the other hand, although structure of plasma density has origin in the particle transport but two distinct steps of the density structure emerge from dominance of collisionality in the source-EEF region and of the Bohm diffusion in the EEF-target region. It is argued and experimental evidence is provided for existence of drift like flute Rayleigh-Taylor in the EEF plasma.

The spatial distribution of the plasma and beam electrons in a region whose extension from a hot cathode is larger than the Debye length, but smaller than the electron mean free path, is analyzed. In addition, the influence of electrons thermionically emitted from a hot cathode and the ratio of electron-to-ion mass on the Bohm velocity and on the ion and electron densities at the plasma-sheath boundary in a gas discharge are studied. It is shown that thermionic emission has the effect of increasing the Bohm velocity, and this effect is more pronounced for lighter ions. In addition, it is shown that the Bohm velocity cannot be increased to more than 24% above its value when there is no electron emission.

Fluid equations with transport effects have been derived from summing up discrete particle effects in the configuration space. The diffusion coefficient takes a form different from, but equivalent to, the Kubo formula. By taking into account the decoherence along the field lines, the diffusive damping in the perpendicular direction, and the finite Larmor radius effect in the cyclotron resonance, it is shown that the diffusion of magnetized 3d plasma has a regime of B−3/2 scaling which lies between the Bohm diffusion of B−1 and the classical diffusion of B−2.

Using the hydrodynamic model and considering a planar geometry, the modified Bohm’s sheath criterion is investigated in a magnetized, collisional plasma consisting of electron and positive ions with finite temperature. It is assumed that the singly charged positive ions enter into the sheath region obliquely, i.e., their velocity at the sheath edge is not normal to the wall, and the electron densities obey Boltzmann relations. It is shown that there are both upper and lower limit for the Bohm entrance velocity of ions in this case and both of these limits depend on the magnitude and direction of the applied magnetic field. To determine the accuracy of our derived generalized Bohm’s criterion, it reduced to some familiar physical condition. Also, using this generalized Bohm’s criterion, the behavior of the electron and positive ion density distributions are studied in the sheath region.

Radiofrequency discharges used in industry often have centrally peaked plasma density profiles n(r) although ionization is localized at the edge, even in the presence of a dc magnetic field. This can be explained with a simple cylindrical model in one dimension as long as the short-circuit effect at the endplates causes a Maxwellian electron distribution. Surprisingly, a universal profile can be obtained, which is self-similar for all discharges with uniform electron temperature Te and neutral density nn. When all collisions and ionizations are radially accounted for, the ion drift velocity toward the wall reaches the Bohm velocity at a radius which can be identified with the sheath edge, thus obviating a pre-sheath calculation. For non-uniform Te and nn, the profiles change slightly but are always peaked on axis. For helicon discharges, iteration with the HELIC code for antenna-wave coupling yields profiles consistent with both energy deposition and diffusion profiles. Calculated density is in absolute-v...

Recent experiments have shown that ions in weakly collisional plasmas containing two ion species of comparable densities approximately reach a common velocity at the sheath edge equal to the bulk plasma ion sound velocity. A recent theory [S. D. Baalrud, C. C. Hegna, and J. D. Callen, Phys. Rev. Lett. 103, 205002 (2009)] suggests that this is a consequence of collisional friction between the two ion species enhanced by the two stream instability. The theory finds that the difference in velocities at the sheath edge depends on the relative concentrations of the two ions. The difference in velocities is small, with both species approaching to the bulk sound velocity, when the concentrations are comparable, and is large, with each species reaching its own Bohm velocity, when the relative concentration differences are large. To test these findings, drift velocities of Ar and Xe ions were measured with laser-induced fluorescence in Ar–Xe and He–Xe plasmas and combined with ion acoustic wave and plasma potential data. In addition, electron temperature was varied by a Maxwell demon [K. R. MacKenzie et al., App. Phys. Lett. 18, 529 (1971)]. The predictions were found to be in excellent agreement with the experimental data. The generalized Bohm criterion in two ion species plasmas is also verified in a wider variety of relative ion concentrations.

Turbulence calculations with a 3D collisional fluid plasma model demonstrate qualitative and semi-quantitative similarity to experimental data in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)], in particular for the temporal spectra, fluctuations amplitude, spatial correlation length, and radial particle flux. Several experimentally observed features of plasma turbulence are qualitatively reproduced, and quantitative agreement is achieved at the order-of-magnitude level. The calculated turbulence fluctuations have non-Gaussian characteristics, however the radial flux of plasma density is consistent with Bohm diffusion. Electric polarization of density blobs does not appear to play a significant role in the studied case. Turbulence spectra exhibit direct and inverse cascades in both azimuthal and axial wavenumbers and indicate coupling between the drift instability and Kelvin-Helmholtz mode.

It is argued that the inclusion of the Bohm potential in quantum fluid equations is equivalent to inclusion of a nonrelativistic form of the quantum recoil in plasma kinetic theory. The Bohm term is incorrect when applied to waves with phase speed greater than the speed of light.

For a collisionless plasma, the magnetic field B enables fluidlike behavior in the directions perpendicular to B; however, fluid behavior along B may fail. The magnetic field also introduces an Alfven-wave nature to flows perpendicular to B. All Alfven waves are subject to Landau damping, which introduces a flow dissipation (viscosity) in collisionless plasmas. For three magnetized plasmas (the solar wind, the Earth’s magnetosheath, and the Earth’s plasma sheet), shear viscosity by Landau damping, Bohm diffusion, and by Coulomb collisions are investigated. For magnetohydrodynamic turbulence in those three plasmas, integral-scale Reynolds numbers are estimated, Kolmogorov dissipation scales are calculated, and Reynolds-number scaling is discussed. Strongly anisotropic Kolmogorov k−5∕3 and mildly anisotropic Kraichnan k−3∕2 turbulences are both considered and the effect of the degree of wavevector anisotropy on quantities such as Reynolds numbers and spectral-transfer rates are calculated. For all three ...

A fluid model is utilized to describe the plasma-sheath boundary for a negatively biased planar probe immersed in electronegative plasmas. The model equations are solved on the scale of the electron Debye length and calculate the spatial distributions of electric potential, velocity, and density of positive ions in front of the probe. The position of sheath edge, the positive ion velocity at sheath edge (the Bohm velocity), and the positive ion flux collected by the probe are determined and compared with analytic (or scaling) formulas. Effects of control parameters on the Bohm velocity, the sheath thickness, and on the positive ion flux are investigated. A larger thermal motion of negative ions causes the Bohm velocity to increase, the sheath to increase, and the positive ion flux collected by the probe to increase. An increase in collision causes the Bohm velocity to decrease and the sheath to decrease resulting in a decrease in the positive ion flux. An increase in electronegativity causes both the Bohm...

We respond to the issues raised in the comment by Maggs and Carter. Our simple model still elucidates the basic physics involved in their experiment. The key point is that, in their geometry, any estimate of the radial ion-diffusion coefficient requires one to evaluate a very small difference of two large quantities, neither of which can be accurately measured or calculated. We stand by our original conclusion that one cannot, with any confidence, state that Bohm diffusion has been observed in the large plasma device experiment.

The results of a recent numerical analysis of a diffusion experiment on the large plasma device (LAPD) [Maggs et al., Phys. Plasmas 14, 052507 (2007)] are re-examined. A simplified analytic solution of the transport equations is obtained by including previously omitted contributions to the transport. This solution strongly suggests that an accurate determination of the perpendicular diffusion coefficient would be very difficult in the specific LAPD experimental arrangement, due to near-cancellation of large terms. Thus, caution should be exercised in claiming that Bohm diffusion, or its suppression in the presence of a large applied radial voltage, has been observed.

The outer region of the plasma column of a large, linear plasma device is rotated in a controlled fashion by biasing a section of the vacuum chamber wall positive with respect to the cathode (Er

N. Sternberg, V. Godyak, and D. Hoffman [Phys. Plasmas 13, 063511 (2006)] have produced a detailed paper on a cylindrical plasma column in an axial magnetic field. The authors found that the radial component of the ion velocity, on leaving the plasma region, is the ion acoustic velocity. This is, of course, the Bohm velocity, but the authors did not comment on this fact. The Bohm criterion does appear to be of general validity, however, and perhaps a greater emphasis should have been given to this result.

Sheaths in low temperature collisionless and weakly collisional plasmas are often viewed as simple examples of nonlinear physics. How well do we understand them? Closer examination indicates that they are far from simple. Moreover, many predicted sheath properties have not been experimentally verified and even the appropriate “Bohm velocity” for often encountered two-ion species plasma is unknown. In addition, a variety of sheathlike structures, e.g., double layers, can exist, and many two- and three-dimensional sheath effects have not been considered. Experimental studies of sheaths and presheaths in weakly collisional plasmas are described. A key diagnostic is emissive probes operated in the “limit of zero emission.” Emissive probes provide a sensitive diagnostic of plasma potential with a resolution approaching 0.1V and a spatial resolution of 0.1cm. Combined with planar Langmuir probes and laser-induced fluorescence, they have been used to investigate a wide variety of sheath, presheath, and sheathlike structures. Our experiments have provided some answers but have also raised more questions.

Experiments are reported where a collissionfree plasma cloud penetrates a magnetic barrier by self-polarization. Three closely related effects, all fundamental for the penetration mechanism, are studied quantitatively: (1) anomalous fast magnetic field penetration (two orders of magnitude faster than classical), (2) anomalous fast electron transport (three orders of magnitude faster than classical and two orders of magnitude faster than Bohm diffusion), and (3) the ion energy budget as ions enter the potential structure set up by the self-polarized plasma cloud. It is concluded that all three phenomena are closely related and that they are mediated by highly nonlinear oscillations in the lower hybrid range, driven by a strong diamagnetic current loop which is set up in the plasma in the penetration process. The fast magnetic field penetration occurs as a consequence of the anomalous resistivity caused by the wave field and the fast electron transport across magnetic field lines is caused by the correlation between electric field and density oscillations in the wave field. It is also found that ions do not lose energy in proportion to the potential “hill” they have to climb, rather they are transported against the dc potential structure by the same correlation that is responsible for the electron transport. The results obtained through direct measurements are compared to particle in cell simulations that reproduce most aspects of the high frequency wave field.