Charged Macroparticles Research Articles

Electrolyte friction on charged spherical macroparticles: Beyond the Debye–Hückel limit

The contribution to the friction coefficient of a charged spherical polyion diffusing in an ionic solution due to its interactions with the electrolyte ions is calculated, in the absence of hydrodynamic interactions, starting from a formal expression for ζel previously derived by Medina-Noyola and Vizcarra-Rendón. It is shown that such a formal expression can be given a particularly simple form in terms of the equilibrium distribution neqi(r) of the small ions around the tracer, which allows us to study effects ignored in Debye–Hückel level theories. We consider, for example, the effect of a finite size of the small ions and nonlinear contributions to ζel on the polyion charge. We show that the correct Debye–Hückel limit differs from Schurr’s result for ζel, and the source of the disagreement is clearly exposed. The results derived here for ζel are not restricted in the number of species of electrolyte ions or in their charges or mobilities.

The Space Charge Computer Program SCHAR

The space charge computer program SCHAR uses macrofilaments or macroparticles to model the effects of space charge in ion transport. The program calculates the transport properties of beams of non-relativistic charged particles using two alternative macroparticle formulations. The line mode formulation considers the beam to be composed of a manageable number of infinitely long charged filaments. The paths of these filaments are fixed in time but their positions as a function of distance along the line are determined by a fourth-order Runge-Kutta time step integration. The point mode formulation considers the beam to be composed of a manageable number of charged macroparticles. These macroparticles have the same charge-to-mass ratio as the actual particles. In this mode the space charge effects are modeled solely by the Coulomb repulsion of the macroparticles. In space charge cases, while the calculation steps from SCHAR are identical, the line mode will run by a factor of two or three times faster than the point mode; if beam bunching occurs, however, use of the line mode becomes inappropriate. Both modes are described by SCHAR in a left-handed Cartesian coordinate system. Among the optional methods for spreading out the filaments or particles in phase space are: four-volumemore » distribution, designed for line mode operation; KV distribution, a specialized four-dimensional input assumed also by TRACE; six-volume distribution, meant for point mode but also applicable to line mode operation; and ''observed'' distribution, designed for point mode operation.« less

Mass-diffusion and self-diffusion properties in systems of strongly charged spherical particles

Using the Fokker–Planck equation as the basic description, various collective and single-particle properties of highly charged spherical macroparticles in solution are derived. The dynamic structure factor S(k,t) for finite k is found to be non-exponential in t due to the viscoelastic properties of the liquid of interacting macroions. By using a mode-coupling procedure the dynamical properties can be completely reduced to the static structure factor S(k), which is calculated according to the method developed by Hansen and Hayter. At short times the system exhibits elastic behaviour and the corresponding high-frequency elastic moduli have been calculated. The bulk modulus is found to increase with c2, where c is the concentration. With regard to the single-particle properties, the velocity autocorrelation function is calculated and from it are obtained the mean-square displacement and the self-diffusion coefficient Ds as a function of concentration and of the coupling strength between macroions.

Dynamic correlations between charged colloidal particles: Coupled macroion–counterion diffusion

A simple theory is presented which predicts the main short-time and long-time features observed in the intermediate scattering function F(k,t) measured in experiments of quasielastic light scattering by suspensions of highly charged polystyrene macroparticles. This theory is based on the description of the coupled diffusion of the macroparticles and their counterions by the linear laws of irreversible thermodynamics, and on the use of spatially nonlocal thermodynamic relations to describe the spatial correlations between the diffusing particles.

Space charge effects in the focusing of intense ion beams

Abstract The use of intense beams of heavy ions to ignite fusion pellets is favoured by the option of the ballistic focusing of these beams in a good vacuum ( −4 Torr) within the target chamber. To achieve the required spot size of a few mm over 10 m distance with reasonabbe beam emittance it is necessary to consider carefully the effect of aberrations on spot size. A non-uniformly distributed space charge may contribute to these aberrations. This effect is studied quantitatively by simulating several thousands of charged macroparticles with a particle-in-cell code using a fast Poisson solver. The optical system consists of two triplets for beam transmission from the periodic transport system to the target. It is found that beam loss by space charge aberration remains below 30% over a wide range of beam currents.

On the Rayleigh Light Scattering from Dilute Solutions of Charged Spherical Macroparticles

On the Rayleigh Light Scattering from Dilute Solutions of Charged Spherical Macroparticles