Larmor radius

The presence of a static magnetic field within a plasma affects microscopic particle motions and microscopic wave motions. The charged particles execute cyclotron motion and their trajectories are altered into helices along the field lines. The radius of the helix, or the Larmor radius, is given by the following ... 

The second method of discrimination uses apertures to intercept some of the scattered flux by virtue of its increased Larmor radius in the magnetic field (e.g. Kauppila et al., 1981 Mizogawa et al, 1985). The extent to which angular discrimination can be provided by this method depends not only on the radius of the aperture, rap, but also on the diameter of the initial beam. Assuming, for simplicity, a beam of particles, each with kinetic energy E, confined to the axis of the system by a uniform magnetic field B, then... 

The different regions are delineated by the Debye length (d), the mean-free path (X), and the Larmor radius rL). In a plasma, there can be many mean-free paths, since there are many different types of particles (different neutral species, electrons and ions). Of primary interest are the mean-free paths for collisions between electrons and heavy particles (Xe) and ions and heavy particles (Xd). 

If a magnetic field exists in a plasma, charged particles will tend to gyrate about magnetic field lines between collisions. The radius of the circular path it takes is called the Larmor radius and is expressed as... 

This means that the Larmor radius of the CM motion is completely determined by the initial distance between the electron and the nucleus in the plane perpendicular to the magnetic field. All amplitudes of the oscillations on the above-mentioned shorter time scales are small compared to this Larmor radius. We note that the above-mentioned effect of the classical self-stabilization of the ion on a Landau orbit is a generic phenomenon for regular phase space, i.e. it occurs for any regular initial conditions. 

The value of D in strong magnetic fields significantly decreases D a I/52, which can be applied to prevent plasma from decaying. Magnetized electrons are trapped by the magnetic field and rotate along the Larmor circles until a collision pushes the electron to another Larmor circle. The electron Larmor radius. 

If there is an electric field and/or the magnetic field is not quite homogeneous (however, the scale length of the inhomogeneity cannot he shorter than the Larmor radius), then there is a slow drift motion of the center of the Larmor circle in the direction perpendicular to hoth the direction of the inhomogeneity and the magnetic field. The value of this drift velocity is ... 

The plasma physics basis for CT reactor projections is derived from MHD stability theory and experimental observations of macrostability, and from postulated transport scaling or scaling of related devices (tokamak and diffuse, toroidal pinch). A central issue, on which different reactor projections can be based, centers on the observed macrostability of certain CT s (reversed field theta-pinch Toroidal apparent contradiction with MHD stability theory. Although the conflict may be resolved by inclusion of finite-ion-larmor radius (FLR) effects in the theory, scaling assumptions to reactor conditions may or may not invoke FLR. 

C. W. Hartman, Finite Larmor Radius Stabilized Z-Pinches, UCID-17118, April 1976. 

Yi2l i2H-2f tancY of First Adiabatic Invar iant. In the weak-field region near the zero line in the plasma interior, violation of the constancy of the first adiabatic invariant takes place, and the Larmor radius tends to infinity at the field zero. The weak-field region is therefore expected to introduce a kind of scattering and diffusion effect which tends to smear out" and stabilize the plasma perturbations. 

Recent experimental results on a compressional Z-pinch and on a laser-initiated gas-embedded Z-pinch show considerable enhancement of MHD stability over conventional theory. It is thought that this could be due to finite ion Larmor radius effects. Several theoretical models of energy and pressure balance of a linear Z-pinch with end-losses have been made electron thermal conduction with (jot = 0, with ojT = oo, and singular thermal ion transit time loss. 

All yield the same essential scaling laws showing that Z-pinch will satisfy Lawson conditions with a current of 10 A, a line density of 10 and a ratio of ion Larmor radius to pinch radius of about... 

W, and burn time 10 s discharge frequencies of 10 s will be required for a 1000 MW plant. The merits of the system are simplicity, scalability to small power stations since the discharges can be arranged in modular form, and no impurity or first wall problems. Further experimental work on compression and laser-initiated gas embedded Z-pinches extending studies to higher currents of 10 A is required, with particular emphasis on large ion Larmor radius stabilisation. 

Let us now take Eq.(4) for the ion Larmor radius a less than a the pinch radius (or radial scale length), and calculate the total guiding centre current of ions, I... 

It is worth emphasising that the singular currents within a Larmor radius of the axis are usually of the same order as the total current, but through diamagnetism the actual current density J, defined by the c.m. velocity, is spread throughout the plasma column. 

The ratio of the average ion Larmor radius to pinch radius for a Z-pinch satisfying the Bennett relation (Eq.(14)) is 8.08 x 10 ... 

N "2, depending only on the line density N. For N = 5.6 x 10 this gives al/a =0.34. It is a remarkable and fortuitous coincidence that under Lawson conditions the ion Larmor radius is comparable with pinch radius and should enhance stability of the pinch. 

The combined results of the two non-adiabatic effects just described yields a net displacement across the F-surfaces, being of the order of one Larmor radius a in the field for a complete particle passage through a support region. The corresponding random-walk process of ions and electrons leads to an equivalent am-bipolar diffusion process across the F-surfaces. The ratio between the corresponding loss rate and the thermonuclear power production Pj)-p has been estimated to ... 

The only ideal MHD modes that are still predicted to be unstable are shown in Fig. 11. The first mode is the same tilting mode predicted and observed in spheromaks. However, this mode has not been observed in highly prolate FRCs with the separatrix radius at least half of the wall radius. The observed stability may be due to kinetic or finite Larmor radius (FLR) effects, or may be a result of the equilibria found in the experiments. The computations have been done for elliptical equilibria (see Fig. 12) while the experiments appear to be more racetrack-like. 

The reason for the stability against the m = 0 could be a favorable plasma pressure profile which satisfies the adiabatic lapse rate. The density measurements show a peak density on axis and a bell-shaped distribution which would go along with this explanation. The kink stability could be produced by finite Larmor radius effects, as well as by reduced growth rates because of the gas blanket. 

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