Collisional Transport in Magnetized Plasmas


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Bohm diffusion is characterized by a diffusion coefficient equal to. It was first observed in by David Bohm , E. Burhop , and Harrie Massey while studying magnetic arcs for use in isotope separation. Fortunately there are exceptions where the diffusion rate is lower, otherwise there would be no hope of achieving practical fusion energy. The diffusion coefficient D can be expressed variously as. Therefore, at least within a factor of order unity, Bohm diffusion is always greater than classical diffusion.

This distinction is often used to distinguish between the two. In light of the calculation above, it is tempting to think of Bohm diffusion as classical diffusion with an anomalous collision rate that maximizes the transport, but the physical picture is different. Anomalous diffusion is the result of turbulence.

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These eddies play a similar role to the gyro-orbits in classical diffusion, except that the physics of the turbulence can be such that the decorrelation time is approximately equal to the turn-over time, resulting in Bohm scaling. The theoretical understanding of plasma diffusion especially the Bohm diffusion remained elusive until the s when Taylor and McNamara [3] put forward a 2d guiding center plasma model.

The concepts of negative temperature state, [4] and of the convective cells [5] contributed much to the understanding of the diffusion. The underlying physics may be explained as follows. The process can be a transport driven by the thermal fluctuations , corresponding to the lowest possible random electric fields.

The low-frequency spectrum will cause the ExB drift. Due to the long range nature of Coulomb interaction, the wave coherence time is long enough to allow virtually free streaming of particles across the field lines. Thus, the transport would be the only mechanism to limit the run of its own course and to result in a self-correction by quenching the coherent transport through the diffusive damping.

The thermal fluctuation is typically a small portion of the particle thermal energy.

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Search Results Results 1 -4 of 4. Cambridge University Press, Ships with Tracking Number! May not contain Access Codes or Supplements. May be ex-library. Buy with confidence, excellent customer service! More tools Find sellers with multiple copies Add to want list. Didn't find what you're looking for? We see on Figure 4 at time indicated 2, that one of the electron vortices reaches the anode.

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This leads to an abrupt decrease of the number of electrons in the system, associated with an electron current pulse on the anode and followed by a complete redistribution of the electron density in the gap. Figure 4. Left: particular sequence in the evolution of electron vortices in the conditions of Figure 3 ; Right: number of electrons as a function of time in the sequence each time of the left plot is indicated by a triangle symbol. Figure 5. Electron current to the anode and to the end plates as a function of time in the conditions of Figures 3, 4.

The variation with time of the total number of electrons in the magnetron is also plotted. The two other vortices are first pushed toward the cathode time 2 , then the outer vortex, close to the anode, merges with one of the two others times 2—3. The two remaining vortex then continue to evolve and grow times 3—5 until each one touches one of the electrodes time 6. They incompletely merge at time 7 and then the system evolves toward a more chaotic distribution of electron density times 8— After some time the density reorganizes and a new system of well-defined electron vortices will emerge.

We see in Figure 5 that the electron current to the anode is composed of large pulses superimposed on a quasi-continuum. The continuum corresponds to the background density of electrons outside the vortices typically 10 times smaller than in the vortices. These electrons slowly flow to the anode through collisional transport across the magnetic field. The pulses correspond to events such as those described above and apparent on Figure 4.

The charged particle losses to the end plates in the direction of the magnetic field play an important role in the overall particle balance. It appears on Figure 5 that there is a clear correlation between the bursts of electron current to the end plates and the electron current pulses to the anode.

This is because each event e. We have also observed situations where the potential in a small region in a vortex or close to a vortex drops below the end plate potential, leading to a large and short electron current pulse to the end plates. The presence of electron vortices in low pressure cylindrical magnetrons and Penning cells has been discussed in the literature mainly by N. Kervalishvili and his group on the basis of current and probe measurements [ 53 — 56 ]. Kervalishvili and his group inferred from their current and probe measurements the presence of the electron vortices and proposed a qualitative description of the formation, interaction, and dynamics of these vortices that is remarkably and strikingly consistent with the PICC MCC simulation results described above.

Kervalishvili et al. The explanation provided by the model is slightly different but not inconsistent with Kervalishvili's interpretation: during the interaction and merging of two vortices, the potential can drop locally close or even below the end plate potential, leading to a short current pulse. If the pressure is raised to around 1 mtorr and above in cylindrical magnetrons of diameter of a few cm, the ion density increases because of collisions while electron trapping by the magnetic field becomes less efficient, and a quasi-neutral plasma forms.


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The magnetron discharge is a glow discharge that can operate at much smaller pressure that non-magnetized glow discharges because of the electron confinement. In a non-magnetized glow discharge without positive column, part of the electrons and ions produced in the negative glow adjacent to the cathode sheath diffuse together toward the anode.

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This ambipolar diffusion is associated with a potential maximum and a field reversal in the glow see, e. In a magnetized glow discharge the collisional electron mobility is smaller than the ion mobility and the sign of the electric field cannot reverse, at least in the context of a simple 1D model of the discharge. Figure 6. Distribution of charged particle densities, ionization rate, and electric field in a 2 cm gap magnetron discharge in argon, 10 mTorr, V, 30 mT, secondary electron emission by ion impact 0.

The large radial plasma electric field seen in Figure 6 , which is necessary to draw the electron current to the anode in the 1D solution, does not form in the 2D solution and the system finds another way to carry the electron current to the anode. The fact that solutions of 1D models of the cylindrical magnetron may not be stable had been discussed by van der Straaten and Cramer [ 62 ] following their publications on 1D PIC MCC simulations [ 60 , 61 ].

This causes a charge separation between electrons and ions and therefore the formation of a perturbed azimuthal electric field. It was shown later by Sakawa et al. We see on this figure that the plasma properties are not azimuthally symmetric. The electric potential in the plasma presents an abrupt azimuthal drop which defines a sharp separation that we call below the front of the instability, or the spoke between two plasma regions.

Ahead of the front in the azimuthal direction, the plasma potential is close to the anode potential V. Behind the front the potential drops abruptly about 10 V over 1—2 mm and reaches a minimum 20 V below the anode potential. Figure 7. The cathode inner cylinder diameter is 1 cm and the anode diameter is 5 cm. The scales are linear and the min, max values are 0, 0. The potential drop in the front is associated with the formation of a double layer. Ions are accelerated azimuthally across the potential drop as can be seen on the distribution of the ion mean energy in Figure 7.

The formation of the spoke allows a complete redistribution of the electron current in the plasma, very different from the simple radial current flow predicted by the 1D model of Figure 6. The abrupt potential drop in the front of the spoke generates a large, quasi-azimuthal electric field as can be inferred from the potential distribution of Figure 7 and is illustrated in Figure 8.

It is interesting to note that the sheath associated with the electric field in the front is directly connected to the anode sheath as can be seen on Figure 8. The lower plasma potential region is surrounded by large electric field layers large electric field in the anode sheath and in the spoke front, lower electric field in the back of the structure. We see that electrons flow from the end of the cathode sheath to the anode in the back of the plasma structure.

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The potential variations are much less abrupt in this region than in the front so the electron flux from cathode to anode is less intense than in the front but is distributed over a large region. The electron flow along the anode sheath turns radially toward the cathode, following the equipotential lines at the location of the spoke, reaches the cathode sheath, follows the cathode sheath edge etc… In term of electron transport from cathode to anode these results can be summarized by saying that there is a large, localized electron flux from anode to cathode at the spoke front, and a smaller but more distributed electron flux from cathode to anode at the back of the cathode.

To have a net flux from cathode to anode, the total electron flow in the back of the structure must be larger than in the front.

go to site Figure 8. Diagram showing the directions of the electric field E and electron mean velocity and flux in the conditions of Figure 7. The equipotential lines in the plasma between V and the anode potential at V are also shown. To better understand the cross-field electron transport from cathode to anode we can measure, in the simulation, the electron current collected by a particular section of the anode as could be done in an experiment with a segmented anode.

This current is shown in Figure 9. We see that the current collected by the anode segment is modulated in time, with a period equal to the period of rotation of the spoke. This current increases when the spoke reaches the anode segment and decreases as the spoke moves away from it. On the ionization rate displayed at three different times in Figure 9 , one can see the larger ionization rate in the spoke region.

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The collected current passes through a maximum just after the spoke has reached the azimuthal position of the collector. Figure 9. Electron current as function of time collected by a segment of the anode indicated by an orange line on the right side of the anode. The positions of the spoke front at the three times can be seen on the ionization rate plots.

Collisional Transport in Magnetized Plasmas Collisional Transport in Magnetized Plasmas
Collisional Transport in Magnetized Plasmas Collisional Transport in Magnetized Plasmas
Collisional Transport in Magnetized Plasmas Collisional Transport in Magnetized Plasmas
Collisional Transport in Magnetized Plasmas Collisional Transport in Magnetized Plasmas
Collisional Transport in Magnetized Plasmas Collisional Transport in Magnetized Plasmas

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