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Uses of Intense Microwaves in Tokamaks
Published in R A Cairns, A D R Phelps, P Osborne, Generation and Application of High Power Microwaves, 2020
When is the Vlasov equation, and hence derivative equations such as the quasilinear diffusion equation, not an appropriate description of a plasma? The only approximation made in deriving the Vlasov equation is in the description of the plasma as a continuum fluid for which a density function is well-behaved. In fact, a plasma is not a continuum fluid at all, rather it is a collection of charged particles. The phase space density is singular where there is a particle and zero where there is not — not a function of which you would care to calculate partial derivatives. But if the scales of interest were large enough, say far larger than the interparticle spacing, then a fluid approximation would seem to be an appropriate description of such a collection, in which case the Vlasov equation follows directly. Another way of stating this condition is that the number of particles in a Debye sphere is very large. The Debye length is the distance over which a plasma shields a charge.
Electrons in Electrolyte
Published in Hualin Zhan, Graphene-Electrolyte Interfaces, 2020
In ambipolar diffusion, charged particles are re-distributed within a shallow layer in plasma at the metal-plasma interface. This layer is the so-called plasma sheath where λD is the Debye length which can be used to represent the thickness of the sheath to an extent, as shown in Fig. 4.1. This concept can be applied to liquid electrolytes where the charged particles are cations and anions, except that an electrical double layer, rather than plasma sheath, is formed. Debye length is defined as the distance at which the potential perturbation caused by an external field/object is screened. When the charged particles follow Boltzmann's statistics in liquids or plasmas, this effect is Debye screening. For the particles (i.e., electrons/holes) in heavily doped semiconductors which are described by Fermi-Dirac distribution, the screening effect is defined as Thomas-Fermi screening, where the screening length is Thomas-Fermi length.
Microscale Plasmas for Metal and Metal Oxide Nanoparticle Synthesis
Published in R. Mohan Sankaran, Plasma Processing of Nanomaterials, 2017
Davide Mariotti, R. Mohan Sankaran
The simplified 0D analysis above provides significant insight into the effect of plasma confinement on the energy balance and local thermodynamic equilibrium. However, plasma confinement has other more complicated implications that are not captured by this analysis. The Debye length is one of the traditional parameters used to characterize plasmas and is given by λD = (εokTe/(neq))1/2, where εo is the electric constant, k is the Boltzmann constant, and q is the elementary charge. If a plasma is confined to a cavity comparable in size to the Debye length, shielding of the charge by the plasma and quasineutrality may no longer be preserved.24 For plasmas with an electron temperature of 3 eV and an electron density of 1016 m–3, a typical Debye length is approximately 10–4 m. Because microplasmas have been found to contain larger electron densities (~1018 m–3) and slightly higher electron temperatures,5,12,18,25,26 a departure from Debye shielding would probably occur at dimensions of 10–4 to 10–5 m. For sustainment to occur at these conditions, a plasma cannot be governed by the same mechanisms as in the case where the Debye length is orders of magnitude smaller than the plasma volume. Therefore, a regime of plasma operation may exist where the conventional definition of Debye length is no longer applicable. When a transition to this new regime occurs, the electron density distribution is incompatible with long-range steady-state plasma neutrality, as established by the Debye length, and the plasma can be sustained and achieved only dynamically.27 Overall, the instantaneous charge imbalance can be used to define the MPR, and the classical definition of a plasma is challenged.9,24
Computational Fluid Dynamics Simulation of Fouling of Plate Heat Exchanger by Phosphate Calcium
Published in Heat Transfer Engineering, 2022
Ulla Ojaniemi, Timo Pättikangas, Ari Jäsberg, Eini Puhakka, Antti Koponen
While immersed in liquid, the solid bodies generally have an electrical surface charge, e.g., due to dissociation of surface groups. The surface charge makes the ions of opposite charge to be redistributed around the bodies. This phenomenon is responsible for the electronic double layer formation in the proximity of the body. For bodies of like sign, the force due to the double layer interactions is repulsive. The electrical double layer interaction is modeled as [16]where ζ1 and ζ2 are the electrical surface potentials for the steel surface and the spherical particle at infinite separation and κ is the inverse of the Debye length. εr is the permittivity of the bulk calculated as temperature dependent [17]. The width of the electrical double layer (Debye length) iswhere Fa is the Faraday constant, I the ion strength, R the gas constant and T the fluid temperature. Debye length is a measure of a charge carrier's net electrostatic effect in solution and describes how far its electrostatic effect persists.
On the stability of shale: the role of zeta potential (ζ) and Debye Hückel length (κ−1) on shale swelling
Published in Petroleum Science and Technology, 2021
Debye Hückel length (κ−1) is the distance to which the particle surface charge and resultant electrical potential is still felt by other charges in the medium. The presence of ions around a charged surface diminishes its electrostatic force and therefore decreases the Debye length (also referred to as screening length). Charges outside the boundary of diffuse double layer is not expected to be affected by electrostatic forces generated by the particle charged surface. Only charges within the diffuse double layer boundary can experience electrostatic forces produced by the particle charged surface.