Particle current density

The attainable particle current density per solid angle of the beam (ions pm s sr ) is an inherent property of the ion source, the so-called brightness. Because of this, reduction of the beam diameter is effected by reducing the beam current. 

Right at the disc the convection current perpendicular to the surface vanishes. The transport to the surface is effected by diffusion so the particle current density jp of any species with concentration c and... 

From Eqs.(14.1) - (14.3), show that the particle current density jp of a species A at a rotating disc can be written in the form ... 

The formula (101) can also be proved with the escape-rate theory. We consider the escape of particles by difffusion from a large reservoir, as depicted in Fig. 17. The density of particles is uniform inside the reservoir and linear in the slab where diffusion takes place. The density decreases from the uniform value N/V of the reservoir down to zero at the exit where the particles escape. The width of the diffusive slab is equal to L so that the gradient is given by Vn = —N/ VL) and the particle current density J = —Wn = VN/ VL). Accordingly, the number of particles in the reservoir decreases at the rate... 

In the above equation, q has been considered to have only one component that is along the -direction. L is the Hermitian Liouville operator, Q = 1 — P, where P is the projector onto the dynamical quantity A . Aa is component of a four-vector of particle current density and particle density, defined as... 

As an example, it is conceivable that in some metal—oxide systems, the cation interstitials entering the oxide at the metal—oxide interface (x = 0) rise to appreciable bulk concentration values C(cl) (0). These defects can then migrate through the oxide layer. Chemical reaction of any such interstitials which happen to reach the oxide—oxygen interface (x = L) will serve to deplete the number at that interface. Thus the bulk concentration C,(d)(L) will be much lower than the number Ccation interstitials from x = 0 to x = L can be expressed as a particle current density J(C1). This particle current density proceeding from the source interface (x = 0) to the sink interface (x — L) can be essentially uniform (i.e. J(ci) independent of position x) if there is no build-up or depletion of the bulk density C(ci) between source and sink. On the other hand, any build-up or depletion of the bulk density C(x) at a position x within the layer will require the current to decrease or increase, respectively, at that position x in order to supply or take away, as the case may be, the requisite number of such defects. 

For growth under an excess of oxygen, an increase of the reactive gas partial pressure leads to a reduction in the deposition rate, which is independent of the substrate temperature. This results from the oxidization of the target, since the metallic particle current density j(Zn) is reduced by the low sputtering yield of the oxidized target. 

It is well known that the particle current density Sjj. in the direction i — k is given by the product of the homogeneous volume concentration n of the migrating particles and their mean velocity caused by the i k transitions. This velocity, however, is equal to the number wjfc of i - k transitions per second multiplied by the path r traversed during each transition. For the reverse transitions k — i one must substitute wjci The resultant particle current density in the direction i k is thus... 

Figure 8. The steady state IV for a double barrier RTD without any DMS layers. The insets are computations for particle current density subject to an ac signal of indicated period, varying from 7.5 kBT to 9.5 kBT.

The particle current density in pair space ja/ (2)(r1,r2) is given by the six-component vector... 

If the velocity distribution F(5, x, t) is known, important macroscopic properties of the electrons can be calculated by appropriate velocity space averaging over the distribution. To give some examples, the density n(x, t), the density of the mean energy u (x, t) and the vectorial particle current density j x, t) of the electrons are given by the averages (Desloge, 1966)... 

As can be seen from the power and momentum balance, Eqs. (46) and (47), a temporal evolution of the mean energy density u, t) and/or of the particle current density j t) is initiated if the instantaneous compensation of the respective gain from the field and the corresponding total loss in collisions is disturbed for any reason. Generally, by collisional dissipation, the electron component tries to reduce these disturbances and to again establish the compensated state in both... 

Furthermore, Fig. 12 illustrates the temporal evolution of the mean energy u ,(t)/n and the reduced particle current density j, t)/n in the neon plasma for the same relaxation processes as are considered in Fig. 9. The mean energy shows a monotone decrease from its initial value m (0)/m U, determined by the... 

By using the same approach and an adequate choice of the boundary condition, the spatial evolution of the electron kinetic quantities can be analyzed in all those space-dependent electric fields that do not reverse their direction with growing z. In such studies, nonconservative inelastic electron collisions can also be included and will cause, in accordance with the consistent particle balance, Eq. (56), a spatial evolution of the particle current density y (z) also. 

The one-particle current-density operator can be generalized for N particles. 

Vq is of the order of 10 s"L Experimentally, it was found that in a solution a concentration gradient of particles in space leads to a particle current density S in the direction from higher concentration to lower concentration given by... 

The particle current density in the presence of the external vector potential /text is given by... 

For the change in particle current density caused by the orbital ip(r, t) we find... 

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