Numerical modeling of low-pressure RF plasmas

A particle-in-cell simulation is used to model the plasma generated in a parallel plate RF reactor at low pressure. Nonperiodic boundary conditions are used, and the electric field and particle motion are obtained by finite-difference methods leading to the self-consistent creation of sheaths on the boundaries. Model cross sections are used to describe collisions between particles. Ionization is included, and the plasma is maintained by fast electrons generated in the RF sheaths. Most of the power dissipation is due to the acceleration of ions in the time-average sheath fields. At high applied voltage, the power dissipation is described well by the power law P∝V^5/2. Simple scaling laws for the density and plasma potential are obtained. The effect of ion mass and charge-exchange colisions on the ion energy spectrum collected by the electrodes is examined. The ion loss rate drops in the presence of charge-exchange collisions, and this leads to an increase in the density. The collisions also markedly alter the ion energy distribution function     

Caging of particles in one-component plasmas

Strongly coupled Coulomb systems are characterized by localization ("caging") of particles trapped and oscillating in slowly fluctuating local potential wells. This observation constitutes the basic assumption underlying the quasilocalized charge approximation. Using molecular dynamics simulation we study the changes in the particles' surroundings (cages) in a classical three-dimensional one-component plasma. The results of our analysis show that at high coupling values, substantial changes occur only after several plasma oscillation cycles. We also analyze the oscillation frequencies of the caged particles and relate the decorrelation of the cages to the process of self-diffusion.     

Scaling characteristics of plasma parameters for low-pressureoxygen RF discharge plasmas

For a low-pressure (1-100 mtorr) oxygen RF discharge plasma, the scaling laws for the densities of charged species such as positive ion, negative ion, and electron are estimated in terms of external and internal plasma parameters for the ion-flux-loss-dominated region based on the global balance equations. The scaling formulas are compared with Langmuir probe measurement results performed on a planar inductively coupled oxygen plasma. The transition point from the ion-flux-loss-dominated region to the recombination-loss-dominated region moves to a lower pressure region as the absorbed power increases     

Variational principle for electrodynamics of moving particles

A consistent relativistic theory of the classical Maxwell field interacting with classical, charged, point-like particles, proposed in [1], is now derived from a variational principle. For this purpose a new electrodynamical Lagrangian based on fluxes is constructed. As a result, we obtain the action principle where i) field degrees of freedom and particle degrees of freedom are kept at the same footing, ii) contrary to the standard formulation, no infinities arise, iii) energy (Hamiltonian) is obtained from the Lagrangian via the Legendre transformation, without any need of adding a complete divergence.     

Electrodynamics of moving particles

A consistent relativistic theory of the classical Maxwell field interacting with classical, charged, point-like particles is proposed. The theory is derived from a classical soliton-like model of an extended particle. An approximation procedure for such a model is developed, which leads to an already renormalized formula for the total four-momentum of the system composed of fields and particles. Conservation of this quantity leads to a theory which is universal (i.e. does not depend upon a specific model we start with) and which may be regarded as a simple and necessary completion of special relativity. The renormalization method proposed here may be considered as a realization of Einstein's idea of deriving equations of motion from field equations. It is shown that the Dirac's 3-dots equation does not describe a fundamental law of physics, but only a specific family of solutions of our theory, corresponding to a specific choice of the field initial data.     

Level populations in plasmas RF discharges and sonic channel

An absolute intensity calibration has been made to previously reported spectrographic measurements in an extensively studied argon rf discharge downstream of the exciting coil, and sonic afterglow. This calibration allows calculation of neutral argon atom density and of individual level population. Neutral atom densities were calculated from the electron density, the electron temperature, and Saha's equation, assuming that the electron temperatures were equal to the excitation temperatures. The densities calculated by these methods were far higher than those obtained from the perfect gas law, the gas temperature, and the pressure. The observed under- population of the ground level is shown to correspond to the “terminal non-equilibrium” defined by PARK.⁽³⁾ The present data are compared with two existing experiments to show that agreement exists among seemingly inconsistent and confusing reports, provided the non-equilibrium phenomena are properly accounted for.     

Screening and attraction of dust particles in plasmas

The potential around a dust particle in a plasma is found using the collisional hydrodynamic equations of dusty plasmas, taking into account ion-dust and ion-neutral collisions and considering the plasma source proportional to the dust density. The linear screening is strongly influenced by the collisions and can substantially differ from Debye screening. Attraction of negatively charged dust particles can occur due to overscreening by the ion fluxes in the presence of friction forces.     

New developments in processing cathodic arc plasmas

Filtering of plasmas by curved solenoidal ducts is well established as a method of removing macroparticles. By analyzing the interactions of planar probes with the drifting plasma of the cathodic arc, new insights have been obtained into the operation of these ducts. Theoretical modeling of these interactions suggests, and experiment confirms, that the use of a separate biased electrode on the inside of the duct gives enhanced transmission without drawing excessive electron current. Theoretical modeling of a negatively biased planar electrode lying parallel to the drift velocity as well as experiment both show that ions are captured effectively onto the electrode producing a macroparticle free film at good deposition rates. The application of pulsed high voltage to the substrate placed at the exit of the duct is treated theoretically, and a model is proposed which gives a good agreement with the experimental concentration profile for a silicon surface coated and simultaneously implanted with titanium     

Mean-field theory of critical phenomenon for mutually repelling particles in complex plasmas

A mean-field theory of criticality for charged particles in complex plasmas is proposed. It is shown that the existence of the critical point and the liquid-vapor coexistence is fully consistent with a purely repulsive potential between particles; the cohesive field due to the plasma background drives these. The critical exponents, calculated by expanding the free energy near the critical point, are found to be classical. The phase coexistence curve, obtained by minimizing Gibbs potential, is similar to that of other mean-field models, e.g., van der Waals fluids, ionic fluids, etc. These results lend support to the concept of "universality" in widely different systems.     

Attraction of positively charged particles in highly collisional plasmas

It is shown that the electrostatic interaction potential between a pair of positively charged particles embedded in a highly collisional plasma has a long-range attractive asymptote. The effect is due to continuous plasma absorption on the particles. The relevance of this result to experimental investigations of complex (dusty) plasmas is discussed.     

Transport of energetic particles by microturbulence in magnetized plasmas

Transport of energetic particles by the microturbulence in magnetized plasmas is studied in gyrokinetic simulations of the ion temperature gradient turbulence. The probability density function of the ion radial excursion is found to be very close to a Gaussian, indicating a diffusive transport process. The particle diffusivity can thus be calculated from a random walk model. The diffusivity is found to decrease drastically for high energy particles due to the averaging effects of the large gyroradius and orbit width, and the fast decorrelation of the energetic particles with the waves.     

The formation of negatively charged particles in thermoemission plasmas

The results of measuring the charges of the magnesium oxide particles formed near a block of metallic magnesium burning in air are presented. It has been found that, apart from positively charged magnesium oxide particles, there are negatively charged particles in the thermoemission plasma of the burning products. It has been shown that within the framework of the model of neutralizing charges, the oxide particles can acquire unlike charges in the thermoemission plasma. The calculations agree with the experimental data.     

A gas target for the study of laser-induced parametric instabilities in plasmas

A hydrogen gas target is described which has been irradiated with a high intensity CO₂ laser beam to study parametric instabilities. Such a target, with n ? n_c, provides considerable flexibility and optical access for detailed diagnostics. Preliminary measurements are reported on stimulated Brillouin (and Compton) scattering, 2-plasmon decay and second harmonic generation, in addition to interferometric and enhanced Thomson scattering measurements, which illustrate the versatility of this target for detailed investigation of parametric instabilities.     

聚变等离子体中高能量粒子驱动的鱼骨模不稳定性研究

在考虑高能量粒子密度的空间分布及箍缩角分布的条件下,建立了研究鱼骨模的色散关系,并作了数值研究。结果表明：当高能量粒子的密度高于某个阈值时,鱼骨模会在高能量粒子密度梯度最大处被激发,其频率与高能量粒子的环向进动频率一致。在高β_h 区间,高能量勉强通行粒子将驱动鱼骨模进入第二稳定区。高能量捕获粒子能激发非共振鱼骨模,与勉强通行粒子激发的鱼骨模类似,在高β_h 区存在第二稳定区。     

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A general dispersion relation for fishbone mode is obtained when spatial density profile and pitch angle profile are taken into account. The fishbone modes can be driven into the second stable regime by barely passing energetic particles in high β_h region. The nonresonant fishbone mode can be induced by trapped energetic particles. Similar to the resonant fishbone modes, the nonresonant fishbone modes can also be driven into the second stable regime by trapped energetic particles and the real frequency linearly increases with increasing β_h.     

Lagrange formalism for particles moving in a space of fractal dimension

Analogs of the Lagrange equation for particles evolving in a space of fractal dimension are obtained. Two cases are considered: 1) when the space is formed by a set of material points (a so-called fractal continuum), and 2) when the space is a true fractal. In the latter case the fractional integrodifferential formalism is utilized, and a new principle for devising a fractal theory, viz., a generalized principle of least action, is proposed and used to obtain the corresponding Lagrange equation. The Lagrangians for a free particle and a closed system of interacting particles moving in a fractal continuum are derived. Zh. Tekh. Fiz. 68, 7–11 (February 1990)     

Chaotic diffusion for particles moving in a time dependent potential well

The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and; (ii) by the solution of the diffusion equation. The dynamic of the diffusing particles is made by the use of a two dimensional, nonlinear area preserving map for the variables energy and time. The phase space of the system is mixed containing both chaos, periodic regions and invariant spanning curves limiting the diffusion of the chaotic particles. The chaotic evolution for an ensemble of particles is treated as random particles motion and hence described by the diffusion equation. The boundary conditions impose that the particles can not cross the invariant spanning curves, serving as upper boundary for the diffusion, nor the lowest energy domain that is the energy the particles escape from the time moving potential well. The diffusion coefficient is determined via the equation of the mapping while the analytical solution of the diffusion equation gives the probability to find a given particle with a certain energy at a specific time. The momenta of the probability describe qualitatively the behavior of the average energy obtained by numerical simulation, which is investigated either as a function of the time as well as some of the control parameters of the problem.