Experimental and theoretical study of density,potential, and current structures of a helium plasma in front of an radio frequency antenna tilted with respect to the magnetic field lines

Potential and density structures in the vicinity of an radio frequency (RF) electrode/antenna in a magnetized plasma are investigated using an RF-compensated cylindrical Langmuir probe. These measurements were performed in the ALINE plasma device in which only electrons can be considered well magnetized. Very precise 2-D maps of the plasma parameters are drawn thanks to a 3-D automatic manipulator on which the probe is mounted. The effect of the tilted magnetic angle between the RF-biased surface and the magnetic lines is also studied thanks to a tilting electrode. Comparison of several simplistic models with the experiments proved the reliability of simple Langmuir probe measurements in such an RF and magnetized environment (space potential vs. tilting angle of the antenna with respect to magnetic field lines and recovery of the floating potential structure using measured currents). A fluid model based on total current density and ion diffusion equations over the biased flux tube provides the same density structures in front of the electrode as the measurements. Those density structures display a “bunny ears” shape and can be explained using transverse RF and collisional current behaviour: In front of the antenna, the transverse ion currents deplete the magnetized flux tube, while at the edge of the biased flux tube, the same currents increase the density.     

Model of magnetically enhanced, capacitive RF discharges

Magnetically enhanced, capacitive RF discharges (called RF magnetrons or MERIE discharges) are playing an increasing role in thin film etching for integrated circuit processing. In these discharges, a weak DC magnetic field is imposed, lying parallel to the powered electrode surface. The authors determine the RF power transferred to the discharge electrons by the oscillating electron sheath in the presence of the magnetic field. Using this, along with particle and energy conservation, they obtain discharge parameters such as the ion flux and ion bombarding energy at the powered electrode as functions of pressure, RF power, and the magnetic field. Some results of the model show good agreement with experiments done on a commercial MERIE system     

Parametric study of 2D potential structures induced by RF sheaths coupled with transverse currents in front of ICRH antenna

Hot-spot formation on the corners of the ICRH antenna can be explained by high DC potential structures, which accelerate ion fluxes and generate strong convective fluxes to the antenna surface. This comes from RF sheaths at the end of open magnetic lines, which rectify RF potential resulting from parallel electric fields. As these electric fields are not homogeneous in front of the antenna, transverse potential gradients generate transverse polarization currents which modify the potential structure. These potentials are studied with a simple flux-tube model and then a 2D-fluid model was elaborated to obtain analytical expressions for rectified potential with respect to these transverse currents. We compare them to numerical results coming from a 2D-fluid code executed in a poloidal plane in front of the antenna. Then we build a potential peak criterion to determine the peaking of DC-potential structures for typical parameters in Tore Supra. Finally, current interaction between different magnetic line lengths is approached.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Investigations on ionic processes and dynamics in the sheath region of helium and hydrogen discharges by laser spectroscopic electric field measurements

Temporally and spatially resolved measurements of the electric field distribution in the sheath region of RF and dc discharges provide a detailed insight into the sheath and ion dynamics. The electric field is directly related to the sheath ion and electron densities, the sheath voltage, and the displacement current density. Under certain assumptions also the electron and ion conduction current densities at the electrode, the ion current density into the sheath from the plasma bulk, the ion energy distribution function, and the power dissipated in the discharge can be inferred. Furthermore, the electric field distribution can give an indication of the collision-induced conversion between different ion species in the sheath. Laser spectroscopic techniques allow the noninvasive in situ measurement of the electric field with high spatial and temporal resolution. These techniques are based on the spectroscopic measurement of the Stark splitting of Rydberg states of helium and hydrogen atoms. Two alternative techniques are applied to RF discharges at 13.56 MHz in helium and hydrogen and a pulsed dc discharge in hydrogen. The measured electric field profiles are analyzed, and the results discussed with respect to the ion densities, currents, energies, temporal dynamics and species composition. Received: 26 July 2000 / Accepted: 12 December 2000 / Published online: 3 April 2001     

Electrical characteristics of argon radio frequency glow dischargesin an asymmetric cell

Measurements of the current and voltage at both electrodes of a parallel-plate, capacitively coupled RF discharge cell (the Gaseous Electronics Conference Reference Cell) were combined with measurements of the voltage on a wire inserted into the glow region between the electrodes, for argon discharges at pressures of 1.3-133 Pa and peak-to-peak applied voltages ⩽400 V. Together, these measurements determined the RF voltage, current, impedance, and power of each sheath of the plasma. Simple power laws were found to describe changes in sheath impedances observed as voltage and pressure were varied. An equivalent circuit model for the electrical behavior of the discharge was obtained. The equivalent circuit model can be used to relate the electrical data to plasma properties such as electron densities, ion currents, and sheath widths. The results differ from models previously proposed for asymmetric RF discharges, and the implications of this disagreement are discussed     

Dependence of resonance condition on pressure in an RF resonancemethod

The plasma density is shown as functions of pressure and magnetic flux density in an RF resonance method using the XPDP1 simulation code. The RF resonance method has the unique feature that a strong electric field in bulk controls the plasma density. Owing to the balance between the electric field decrease and the collision rate increase, the plasma density in the RF resonance method has a peak with respect to pressure. The plasma density with respect to the magnetic flux density depends on the condition of the RF resonance method, and the dependence is strong at low pressure because of the strong resonance. Sheath thickness is the most important parameter that determines the strength of the resonance induced. It is shown that the sheath thickness s is related to the plasma density n as a function of ns, obtained from a dispersion relation at constant external parameters. The magnetic flux density which induces the strong resonance is determined from sheath thickness. The plasma density in the RF resonance method can be predicted from discharge parameters using the relation between plasma density and sheath thickness     

Numerical study on discharge characteristics influenced by secondary electron emission in capacitive RF argon glow discharges by fluid modeling

A one-dimensional(1D) fluid model of capacitive RF argon glow discharges between two parallel-plate electrodes at low pressure is employed. The influence of the secondary electron emission on the plasma characteristics in the discharges is investigated numerically by the model. The results show that as the secondary electron emission coefficient increases,the cycle-averaged electric field has almost no change; the cycle-averaged electron temperature in the bulk plasma almost does not change, but it increases in the two sheath regions; the cycle-averaged ionization rate, electron density, electron current density, ion current density, and total current density all increase. Also, the cycle-averaged secondary electron fluxes on the surfaces of the electrodes increase as the secondary electron emission coefficient increases. The evolutions of the electron flux, the secondary electron flux and the ion flux on the powered electrode increase as the secondary electron emission coefficient increases. The cycle-averaged electron pressure heating, electron Ohmic heating, electron heating, and ion heating in the two sheath regions increase as the secondary electron emission coefficient increases. The cycle-averaged electron energy loss increases with increasing secondary electron emission coefficient.     

Electric field measurements and computational modeling at ultrahigh-field MRI

While magnetic resonance images essentially contain a map of the both circularly polarized components of the RF transverse magnetic fields (B(1) field), the thermal heat and electromagnetic power deposition is generated by the associated electric fields. Measurement of electric field distributions/intensities across a sample yields an indirect indication of possible cause of heating within the sample and potentially enables the detection of "hot spots," which can be present within inhomogeneous radiofrequency (RF) fields, such as the case with magnetic resonance imaging at high field strength. As a result, establishing a valid technique for direct measurements of the electric field and its correlation, obtained using computational electromagnetics, is essential in assessing (1) the safety of the RF coil designs and (2) the validity of the calculations. In this work, a probe was built and used to measure the transverse electric field (E(1) field) distributions within an empty 8 T (tuned to 340 MHz) RF head coil and within a saline water phantom loaded in the same coil. The measured E(1) field distributions were favorably compared to the distributions obtained utilizing a finite difference time domain in-house package.     

Power absorption corresponding to ion losses in parallel-plate RFdischarges

A simple model of a symmetric parallel-plate RF discharge is studied to illustrate how such discharges may absorb power from an RF power supply in order to sustain DC power losses corresponding to the steady acceleration of ions through the sheaths. The motions of the sheath boundaries over one period are derived assuming that the current density varies sinusoidally. One finds that the sheath thickness increases discontinuously at one sheath whenever the plasma contacts the opposing electrode. This implies that the external power supply delivers an electron pulse from the electrode at higher potential to the electrode at lower potential, so that some power is being absorbed in a pulsed fashion. The power absorbed by the discharge is also calculated for the portions of the RF cycle where the current varies sinusoidally. It is found that power is supplied by the discharge in this phase of the RF cycle, with the energy coming from the deflating sheaths. It is further shown that the sum of the pulsed power absorption and smooth power generation, averaged over one RF period, is equal to the DC ion power losses arising from ions falling through the time-averaged sheath potentials     

2 cm电子回旋共振离子推力器离子源中磁场对等离子体特性与壁面电流影响的数值模拟

电子回旋共振离子推力器(electron cyclotron resonance ion thruster,ECRIT)离子源内等离子体分布会影响束流引出,而磁场结构决定的ECR区与天线的相对位置共同影响了等离子体分布.在鞘层作用下,等离子体中的离子或电子被加速对壁面产生溅射,形成壁面离子或电子电流,造成壁面磨损和等离子体损失,因此研究壁面电流与等离子体特征十分重要.为此本文建立2 cm ECRIT的粒子PIC/MCC(particle-in-cell with Monte Carlo collision)仿真模型,数值模拟研究磁场结构对离子源内等离子体与壁面电流特性的影响.计算表明,当ECR区位于天线上游时,等离子体集中在天线上游和内外磁环间,栅极前离子密度最低,故离子源引出束流、磁环端面电流和天线壁面电流较低.ECR区位于天线下游时,天线和栅极上游附近的等离子体密度较高,故离子源引出束流、天线壁面电流和磁环端面电流较高.腔体壁面等离子体分布与电流受磁场影响最小.     

RF discharge in the transverse magnetic field numerical model

A numerical model of RF discharges in a steady transverse magnetic field is developed. This model is valid in a range of parameters (gas pressure, magnetic field, RF voltage) used in a number of experimental and technical installations. The comparison between numerical calculations and some experimental results is presented     

Rashba-induced transverse pure spin currents in a four-terminal quantum dot ring

By applying a local Rashba spin–orbit interaction to an individual quantum dot of a four-terminal four-quantum-dot ring and introducing a finite bias between the longitudinal terminals, we theoretically investigate the charge and spin currents in the transverse terminals. It is found that when the quantum dot levels are separate from the chemical potentials of the transverse terminals, notable pure spin currents appear in the transverse terminals with the same amplitude but opposite polarization directions. In addition, the polarization directions of such pure spin currents can be inverted by altering the structure parameters, i.e., the magnetic flux, the bias voltage, and the values of quantum dot levels with respect to the chemical potentials of the transverse terminals.     

Reactor modeling of magnetically enhanced capacitive RF discharge

Magnetic and collisional effects on capacitive radio frequency (RF) discharges for magnetically enhanced reactive ion etching (MERIE) are investigated. Using simplified plasma and sheath models, a collisional magnetic-sheath equation that governs the sheath dynamics under a de magnetic field crossed with a sinusoidal RF electric field is obtained. The sheath equation includes global effects of the bulk plasma. Together with the power-balance equation and the particle-conservation equation, the sheath equation is used to extract a circuit model and predict the electrical behavior of MERIE reactors. Numerical results on the plasma density and the power in MERIE reactors agree well with reported experimental results and the circuit model describes the repeated discharge properties well     

Ion Flux from the Cathode Region of a Vacuum Arc

This paper reviews the properties of the cathode ion flux generated in the vacuum arc. The structure and distribution of mass erosion from individual cathode spots and the characteristics of current carriers from the cathode region at moderate arc currents are described. An appreciable ion flux (～10% of total arc current) is emitted from the cathode of a vacuum arc. This ion flux is strongly peaked in the direction of the anode, though some ion flux may be seen even at angles below the plane of the cathode surface. The observed spatial distribution of the ion flux is expressed quite well as an exponential function of solid angle. The ion flux is quite energetic, with average ion potentials much larger than the arc voltage, and generally contains a considerable fraction of multiply-charged ions. The average ion potential and ion multiplicity increase significantly for cathode materials with higher arc voltages, but decrease with increasing arc current for a particular material. The main theories concerning ion acceleration in cathode spots are the potential hump theory (PH), which assumes that all ions are created at the same potential, and the gas dynamic theory (GD), which assumes that all ions are created with the same flow velocity. Experimental data on the potentials and energies of individual ions indicates that these theories in their original forms are not quite correct, however extensions or modifications of the PH and GD theories seem very likely to be able to predict correct values for the charge states, potentials, and energies of individual ions.     

Auxiliary phase encoding in multi spin-echo sequences: application to rapid current density imaging

Multi spin-echo sequences such as single-shot RARE are very sensitive to the initial phase of the transverse magnetization, and they can preserve only the transverse magnetization component which is aligned with the axis of the refocusing pulse rotation. Therefore, two separate single-shot RARE experiments with phases of refocusing pulses 90 degrees apart have to be run and their complex images summed to obtain an error-free phase map of the initial transverse magnetization. This is particularly useful when auxiliary phase encoding is integrated in the preparation period of the RARE sequence, such as when encoding flow, displacement, susceptibility, pH or temperature. In this paper, the two-shot RARE approach is verified first theoretically and then experimentally by demonstrating its application to rapid current density imaging (CDI). The sequence consists of the preparation period which triggers electric pulses in the sample followed by the RARE acquisition period. Electric currents through the sample induce a magnetic field change in the direction of the static magnetic field and a phase change of the initial magnetization proportional to it. To calculate one component of current density two orthogonal components of magnetic field change must be measured. In general, for 2D non-symmetrical samples, this can be done by rotating the sample to a perpendicular orientation. The proposed CDI method allows much for faster magnetic field change mapping than the standard spin-echo based CDI.     

Ion flux from the cathode region of a vacuum arc

The properties of the ion flux generated in a vacuum arc are reviewed. The structure and distribution of mass erosion from individual cathode spots and the characteristics of current carriers from the cathode region at moderate arc currents are described. An appreciable ion flux (~10% of the total arc current) is emitted from the cathode of a vacuum arc. This ion flux is strongly peaked in the direction of the anode, although some ion flux may be seen even at angles below the plane of the cathode surface. The observed spatial distribution of the ion flux is expressed quite well as an exponential function of the solid angle. The ion flux is quite energetic, with average ion potentials much larger than the arc voltage, and generally contains a considerable fraction of multiply charged ions. The average ion potential and ion multiplicity increase significantly for cathode materials with higher arc voltages but decrease with increasing arc current for a particular material. The main theories concerning ion acceleration in cathode spots are the potential hump theory and the gas dynamic theory. Experimental data indicate that these theories serve reasonably well when used to predict the mean values of the charge state, ion potential, and ion energies for the ion flux, but are quite insufficient when compared with the results for the potentials and energies of individual ions     

射频爆磁压缩发生器小型化共形天线

射频爆磁压缩发生器作为一次性电磁脉冲产生和辐射的小型化装置,其辐射天线的结构和性能是其在实用化层面亟待突破的瓶颈。针对这一问题,深入研究了射频爆磁压缩发生器产生和辐射电磁脉冲的机理,并在此基础上,提出了一种适于实际需求的射频爆磁压缩发生器小型化共形天线。此共形天线设计成爆磁压缩发生器本体的一部分,在结构方面保证了该装置的小型化和实用性。CST仿真和实物测试结果表明,此共形天线在0.5 GHz到10.3 GHz的频带上具有良好的辐射特性,在辐射性能方面同样可以满足射频爆磁压缩发生器实用性的需求。     

A study of methods for moving particles in RF processing plasmas

Methods for moving charged particles in RF processing plasmas are investigated. These methods include varying RF power, varying chamber pressure, attraction and repulsion by an electrostatic probe, and movement with magnetic fields. Varying RF power changes the depth of the potential wells where particles are trapped. The RF power affects shape and location of the traps and the bulk plasma potential. Increasing the chamber pressure moves the sheath edge closer to the wafer being processed. Since particle traps are found at the plasma sheath edge increasing the chamber pressure will move the particle traps (and any trapped particles) closer to the wafer being processed. The Langmuir probe can repel particles when under negative bias and attract them when positively biased. This probe can also distort the sheath edge when the tip resides within the sheath. Applying a magnetic field can change the characteristics of the particle traps and produce a force on the charged dust particles     

String behaviour of magnetic field lines and their rotation in neutron star’s interior

It is found from Maxwell’s equations that the magnetic field lines are good analogues of relativistic strings. The Lorentz force per unit length of magnetic tube is interpretable as Magnus force acting on each individual magnetic tube. It is shown that the superconducting current in pulsar’s interior causes local rotation of magnetic flux tubes carrying quantized flux. Such local rotation remains operative as long as the induced magnetic field of normal electron fluid is above the lower critical field but below the upper. The conservation of magnetic flux leads to a geometrical condition in the form of the Weingarten identity which ensures the existence of family of “magnetic world sheetrdquo;. Each “magnetic world sheet” is a magnetic flux conserving surface. In the process of collapse, a compact spacelike cross-section of a magnetic tube terminates into a trapped surface if the magnetic energy grows faster along the fluid flow lines than that along the magnetic field lines.     

Modulation of Spin Distribution and Spin Transport by a Magnetic Field in a Quasi-One-Dimensional System with Spin--Orbit Coupling

The distributions of spin and currents modulated by magnetic field in a transverse parabolic confined two-dimensional electronic system with a Rashba spin--orbit coupling have been studied numerically. It is shown that the spin accumulation and the spin related current are generated by magnetic field if the spin--orbit coupling is presented. The distributions of charge and spin currents are antisymmetrical along the cross-section of confined system. A transversely applied electric field does not influence the characteristic behaviour of charge- and spin-dependent properties.