Drift Velocity Of Particles Research Articles

Two-Dimensional, Time-Independent Solutions for Plasma Moving through a Uniform Transverse Magnetic Field

If particle gyroradii and drift velocities are small in a collisionless plasma which is infinite and uniform in the direction of the straight magnetic field B, it may be shown in the time-independent case that particle densities and B are constant on any surface of constant electrostatic potential. Using the magnetohydrodynamic equation of motion, it follows that the particles move very nearly along these equipotential surfaces, and an expression for the charge density may be derived. From the resulting Poisson equation, solutions for plasma crossing a uniform B0 field may be obtained; collectively these solutions may appropriately be termed the ``double-vortex'' model from their drift velocity patterns.

The drift velocity of trapped particles

The longitudinal drift velocity of a particle trapped in the earth's field is conconsidered. It is shown that there is a relation between drift velocities at different points on any line of force and that the drift velocities of particles with different mirror points are also related. These relations can be used to simplify the calculation of the average effects of the atmosphere.

Motion of magnetic lines of force

It is often said that magnetic lines of force in a conducting fluid move with the fluid. In the case of a plasma, this means that the lines of force move with the particle drift velocity 1 v p = ( E × H) H 2 . Such statements are not directly verifiable, since the velocity of a line of force is not a measurable quantity. However, the statement that the lines of force move with a certain velocity v(r, t) does have verifiable consequences, such as: (1) The flux through a closed curve moving with velocity v is constant. (2) A line, moving with velocity v, which is initially a line of force, remains a line of force in the course of its motion. Statement (2), as well as all other verifiable consequences of the original hypothesis, follows from statement (1). A velocity is said to be flux-preserving if it satisfies (1), line-preserving if it satisfies (2). It is permissible to ascribe a velocity v to the lines of force if and only if ∇ × (E + v × H) vanishes identically. It is always possible to choose a v satisfying this relation, although it is not generally possible to do this uniquely. To say that a certain velocity v is permissible means that all the verifiable consequences of ascribing this velocity to the lines of force are valid, i.e., that v is flux-preserving. In the case of the particle drift velocity the condition for flux-preservation reduces to ∇ × [ H(E·H) H 2 ] = 0 . Even if v p is not flux-preserving, there may be some closed curves moving with velocity v p which have constant flux. A semiexhaustive enumeration of such curves is given for a general electromagnetic field. Among these curves are those which lie in a surface everywhere perpendicular to H, if this surface is independent of time. A family of such surfaces will exist if and only if H·∇ × H and H × Ḣ both vanish identically. A velocity may be line-preserving without being flux-preserving, but not vice versa. The necessary and sufficient condition for line-preservation is that H × [∇ × (E + v × H)] should vanish identically. The motion of the lines of force in a plasma is related only to the transverse motion of the charged particles. The latter is separable from the longitudinal motion if and only if v p is line-preserving. A necessary and sufficient condition is also given for the separability of only one component of the transverse motion. The concept of a line of force is not relativistically covariant, because each point of a line of force has the same time coordinate. A curve in space-time which appears as a line of force in one frame of reference will therefore not be a line of force in another frame of reference. However, a moving line of force will trace out a two-dimensional surface in space-time, and it may be that this surface will intersect every space-like hyperplane in a line of force. In that case the surface will appear as the path of a moving line of force in every frame of reference, thus defining a moving line of force as a covariant concept. It is shown that a family of such surfaces exists if and only if E·H vanishes identically, in which case they will be generated by lines of force moving with the particle drift velocity v p .

A new approach to the theory and operation of electrostatic precipitators for use on pulverized-fuel-fired boilers

The paper discusses the experience gained and the results of experiments performed whilst endeavouring to obtain satisfactory performance from electrostatic precipitator plant.The principal factors determining drift velocity in precipitators are discussed. A simple approximate relation for the field strength in a parallel-plate horizontal-flow precipitator is developed, based on that generally accepted for a wire-in-cylinder precipitator unit.Comprehensive expressions are introduced for calculating the theoretical performance of precipitators under conditions of nonuniform gas flow and with dust of mixed composition. It is shown that individual drift velocities for different particles may be determined from appropriate experimental observations.The suggestion that pulverized fuel dust is composed largely of two distinct types of particles, one wholly ash and the other coal minus volatiles, i.e. coke, is discussed. Evidence, principally from South African sources, is put forward to support this suggestion.The effective drift velocities obtained in practice for plants operating on Natal duff coal are calculated for a given field strength and are compared with those measured elsewhere. Separate drift velocities for average ash and coke particles are given, and the former are shown to have higher useful drift speeds than the latter.It is shown that, as predicted in theory and as previously proved under laboratory conditions, the drift velocities of particles of the sizes encountered in practice do, in fact, increase with the particle diameter, given a constant composition.Finally, notes are included on the interpretation of test data in order to locate and correct the more common sources of poor performance of precipitators.