A steady-state model of current filamentation caused by the electrothermal instability in a fully ionized magnetized plasma

1982 ◽  
Vol 27 (3) ◽  
pp. 427-435 ◽  
Author(s):  
M. G. Haines ◽  
F. Marsh
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Ohmic Heating ◽  
Maximum Growth ◽  
Energy Balance Equation ◽  
Critical Value ◽  
Magnetized Plasma ◽  
Larmor Radius ◽  
Ion Temperature ◽  
Acoustic Instabilities

A magnetically confined two-fluid plasma is considered in which the Ohmic heating of the electrons by a current driven parallel to an applied magnetic field is balanced by bremsstrahlung and equipartition to the ions. It is found that for a steady state the applied electric field must be below a critical value which in absence of bremsstrahlung is given by where the electrical conductivity is and the total pressure is p. Under this condition it is found that there are two /Futions for Te/Ti which satisfy the steady electron energy balance equation in a homogeneous, fully ionized plasma. One of these /Futions always has values above the critical value of Te/Ti (= 132 in absence of bremsstrahlung) for the onset of the electrothermal instability in a fully ionized gas. Inclusion of electron thermal conduction transverse to the magnetic field (with Hall parameter ) yields a wavelength for maximum growth of the instability of about , where ae is the electron Larmor radius. The steady non linear profiles showing current filamentation have been calculated. Runaway electrons and ion-acoustic instabilities can occur in the spatial maximum of the current density and electron temperature. Inclusion of bremsstrahlung loss reduces the value of Te/Ti for the onset of the instability, and at Te = Ti yields a maximum ion temperature obtainable by Ohmic heating in a stable plasma.

Induction Suspension of Conductive Microring and Its Gyroscopic Stabilization

2021 ◽  
Author(s):  
Dmitrii Skubov ◽  
Ivan Popov ◽  
Pavel Udalov
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Eddy Current ◽  
Equilibrium Position ◽  
Critical Case ◽  
Conservative System ◽  
Critical Value ◽  
Main Task ◽  
Gyroscopic Stabilization

Abstract The main task of our work is determination of possible levitation of micro-ring with eddy current in magnetic field of down ring with set alternating current and determination of critical value of «ohmic» damping separated field of parameters, at which motions of suspension ring transit from divergent to meeting to steady-state equilibrium position. I. e. in this critical case the motion practically coincides with motions of conservative system. The possibility of gyroscopic stabilization of suspension ring taking into account initial set rotation is considered. Thereby it can serve as contactless micro-gyroscope.

scholarly journals Dependence on ion temperature of shallow-angle magnetic presheaths with adiabatic electrons

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
Alessandro Geraldini ◽  
F. I. Parra ◽  
F. Militello
Keyword(s):  
Magnetic Field ◽  
Fluid Model ◽  
Boltzmann Distribution ◽  
Distribution Functions ◽  
Magnetized Plasma ◽  
Electron Mass ◽  
Ion Temperature ◽  
Ion Distribution ◽  
Ionic Charge ◽  
The Magnetic Field

The magnetic presheath is a boundary layer occurring when magnetized plasma is in contact with a wall and the angle $\unicode[STIX]{x1D6FC}$ between the wall and the magnetic field $\boldsymbol{B}$ is oblique. Here, we consider the fusion-relevant case of a shallow-angle, $\unicode[STIX]{x1D6FC}\ll 1$ , electron-repelling sheath, with the electron density given by a Boltzmann distribution, valid for $\unicode[STIX]{x1D6FC}/\sqrt{\unicode[STIX]{x1D70F}+1}\gg \sqrt{m_{\text{e}}/m_{\text{i}}}$ , where $m_{\text{e}}$ is the electron mass, $m_{\text{i}}$ is the ion mass, $\unicode[STIX]{x1D70F}=T_{\text{i}}/ZT_{\text{e}}$ , $T_{\text{e}}$ is the electron temperature, $T_{\text{i}}$ is the ion temperature and $Z$ is the ionic charge state. The thickness of the magnetic presheath is of the order of a few ion sound Larmor radii $\unicode[STIX]{x1D70C}_{\text{s}}=\sqrt{m_{\text{i}}(ZT_{\text{e}}+T_{\text{i}})}/ZeB$ , where e is the proton charge and $B=|\boldsymbol{B}|$ is the magnitude of the magnetic field. We study the dependence on $\unicode[STIX]{x1D70F}$ of the electrostatic potential and ion distribution function in the magnetic presheath by using a set of prescribed ion distribution functions at the magnetic presheath entrance, parameterized by $\unicode[STIX]{x1D70F}$ . The kinetic model is shown to be asymptotically equivalent to Chodura’s fluid model at small ion temperature, $\unicode[STIX]{x1D70F}\ll 1$ , for $|\text{ln}\,\unicode[STIX]{x1D6FC}|>3|\text{ln}\,\unicode[STIX]{x1D70F}|\gg 1$ . In this limit, despite the fact that fluid equations give a reasonable approximation to the potential, ion gyro-orbits acquire a spatial extent that occupies a large portion of the magnetic presheath. At large ion temperature, $\unicode[STIX]{x1D70F}\gg 1$ , relevant because $T_{\text{i}}$ is measured to be a few times larger than $T_{\text{e}}$ near divertor targets of fusion devices, ions reach the Debye sheath entrance (and subsequently the wall) at a shallow angle whose size is given by $\sqrt{\unicode[STIX]{x1D6FC}}$ or $1/\sqrt{\unicode[STIX]{x1D70F}}$ , depending on which is largest.

Dense plasma in Z-pinches and the plasma focus

1981 ◽  
Vol 300 (1456) ◽  
pp. 649-663 ◽  
Keyword(s):  
Magnetic Field ◽  
Plasma Focus ◽  
Axial Magnetic Field ◽  
Ohmic Heating ◽  
Scaling Law ◽  
Three Dimensional ◽  
Power Input ◽  
Larmor Radius ◽  
Mass Motion ◽  
Enhanced Stability

Many of the earliest experiments in controlled thermonuclear fusion research were Z -pinches. However these pinches were found to be highly unstable to the m = 0, the m — 1 (kink), and the Rayleigh-Taylor instability. The addition of an axial magnetic field and the removal of end losses by proceeding to a toroidal geometry has led to the class of discharges known as tokamaks and the reversed field pinch. But, at fusion temperatures and with practical values of applied magnetic field this restricts the plasma density to 10 20 to 10 21 m- 3 , thereby requiring a containment time of several seconds and a plasma radius of about 1 m. Meanwhile studies of the plasma focus, which after its three-dimensional compression closely resembles a Z -pinch, have shown that a plasma of density 10 25 m- 3 and temperature 1 keV can be achieved in a narrow filament of radius 1 mm. It has enhanced stability properties which might be attributable to the effects of finite ion Larmor radius. Its neutron yield in deuterium can be as high as 10 12 per discharge, with a favourable empirical scaling law, but the thermonuclear origin of the neutrons is doubtful because of the evidence of centre-of-mass motion and the formation of electron and ion beams. The development of high voltage, high current pulse technology has permitted the reconsideration of the Z -pinch to attain dense fusion plasmas which might be stabilized by scaling the ion Larmor radius to be comparable with the pinch radius. Experiments at Imperial College show that the plasma remains stationary for about twenty Alfven radial transit times, limited only by the period of the current waveform. Theory indicates that a dense compact Z -pinch can satisfy Lawson conditions with a power input dependent on the enhanced stability time, or, if stable, with ohmic heating balancing axial heat losses. Preliminary results on a laser-initiated Z -pinch are also presented.

scholarly journals ESTIMATES OF BLOW-UP TIME FOR A NON-LOCAL REACTIVE–CONVECTIVE PROBLEM MODELLING OHMIC HEATING OF FOODS

2006 ◽  
Vol 49 (1) ◽  
pp. 215-239 ◽  
Author(s):  
C. V. Nikolopoulos ◽  
D. E. Tzanetis
Keyword(s):  
Steady State ◽  
Initial Data ◽  
Blow Up ◽  
Ohmic Heating ◽  
Steady State Solution ◽  
Critical Value ◽  
Stationary Solutions ◽  
State Solution ◽  
Non Local ◽  
The Difference

AbstractIn this work, we estimate the blow-up time for the non-local hyperbolic equation of ohmic type, $u_t+u_{x}=\lambda f(u)/(\int_{0}^1f(u)\,\mathrm{d} x)^{2}$, together with initial and boundary conditions. It is known that, for $f(s)$, $-f'(s)$ positive and $\int_0^\infty f(s)\,\mathrm{d} s\lt\infty$, there exists a critical value of the parameter $\lambda>0$, say $\lambda^\ast$, such that for $\lambda>\lambda^\ast$ there is no stationary solution and the solution $u(x,t)$ blows up globally in finite time $t^\ast$, while for $\lambda\leq\lambda^\ast$ there exist stationary solutions. Moreover, the solution $u(x,t)$ also blows up for large enough initial data and $\lambda\leq\lambda^\ast$. Thus, estimates for $t^\ast$ were found either for $\lambda$ greater than the critical value $\lambda^\ast$ and fixed initial data $u_0(x)\geq0$, or for $u_0(x)$ greater than the greatest steady-state solution (denoted by $w_2\geq w^*$) and fixed $\lambda\leq\lambda^\ast$. The estimates are obtained by comparison, by asymptotic and by numerical methods. Finally, amongst the other results, for given $\lambda$, $\lambda^*$ and $0\lt\lambda-\lambda^*\ll1$, estimates of the following form were found: upper bound $\epsilon+c_1\ln[c_2(\lambda-\lambda^*)^{-1}]$; lower bound $c_3(\lambda-\lambda^*)^{-1/2}$; asymptotic estimate $t^\ast\sim c_4(\lambda-\lambda^\ast)^{-1/2}$ for $f(s)=\mathrm{e}^{-s}$. Moreover, for $0\lt\lambda\leq\lambda^*$ and given initial data $u_0(x)$ greater than the greatest steady-state solution $w_2(x)$, we have upper estimates: either $c_5\ln(c_6A^{-1}_0+1)$ or $\epsilon+c_7\ln(c_8\zeta^{-1})$, where $A_0$, $\zeta$ measure, in some sense, the difference $u_0-w_2$ (if $u_0\to w_2+$, then $A_0,\zeta\to0+$). $c_i\gt0$ are some constants and $0\lt\epsilon\ll1$, $0\ltA_0,\zeta$. Some numerical results are also given.

Instability of obliquely propagating dust waves in a collisional highly magnetized plasma

2007 ◽  
Vol 73 (2) ◽  
pp. 189-197 ◽  
Author(s):  
M. ROSENBERG ◽  
P.K. SHUKLA
Keyword(s):  
Magnetic Field ◽  
Magnetized Plasma ◽  
Charged Dust ◽  
Experimental Conditions ◽  
Electrostatic Waves ◽  
Current Instability ◽  
Acoustic Instabilities ◽  
The Magnetic Field ◽  
Thermal Speed ◽  
Field Drift

Abstract.We investigate the instability of obliquely propagating dust waves in a collisional, magnetized plasma containing negatively charged dust grains. It is assumed that the magnetic field strength is such that the ions and electrons are magnetized, while the dust is unmagnetized. We consider both modified two-stream and dust-acoustic instabilities that are driven by an ion cross-field drift and that occur for waves propagating obliquely to the magnetic field. We use parameters that may be representative of possible laboratory experimental conditions to illustrate the growth rates. We also compare our results with prior theoretical studies of a Hall current instability of perpendicularly propagating electrostatic waves. It is found that these obliquely propagating wave instabilities may also be important for representative laboratory parameters when the cross-field drift speed is a significant fraction of the ion thermal speed.

scholarly journals Brillouin-shifted third-harmonic backscattering of laser in a magnetized plasma

2015 ◽  
Vol 33 (1) ◽  
pp. 97-102 ◽  
Author(s):  
Alireza Paknezhad
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Static Magnetic Field ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Magnetized Plasma ◽  
Third Harmonic ◽  
Coupled Equations ◽  
Relativistic Mass ◽  
Weakly Coupled

AbstractThird-harmonic Brillouin backscattering (3HBBS) instability is investigated in the interaction of a picosecond extraordinary laser pulse with a homogeneous transversely magnetized underdense plasma. Nonlinear coupled equations that describe the instability are derived and solved for a weakly coupled regime to find the maximum growth rate. The nonlinearity arises through the combined effect of relativistic mass increase, static magnetic field, and ponderomotive acceleration of plasma electrons. The growth rate is found to decrease as the static magnetic field increases. It also increases by increasing both plasma density and laser intensity. It is also established that the growth rate of 3HBBS instability in a magnetized plasma is lower than that of fundamental Brillouin backscattering instability.

ORBIT ANALYZER PROBES FOR THE MEASUREMENT OF PLASMA TEMPERATURES

1967 ◽  
Vol 45 (9) ◽  
pp. 3055-3064 ◽  
Author(s):  
D. J. Loughran ◽  
L. Schott ◽  
H. M. Skarsgard
Keyword(s):  
Magnetic Field ◽  
Debye Length ◽  
Current Collector ◽  
Boltzmann Distribution ◽  
Electron Velocity ◽  
Larmor Radius ◽  
Ion Temperature ◽  
Magnetic Analyzer ◽  
Current Characteristics ◽  
The Magnetic Field

An investigation is presented of two different probes, of the magnetic analyzer type, in which the magnetic field used for analysis of the particle orbits is also present in the plasma. Both probes employ a current collector whose distance from the aperture plane is adjustable. One probe (the charge-selective probe) collects charged particles of one sign, while theother (the charge-insensitive probe) collects particles of both signs. Assuming a Maxwell–Boltzmann distribution of electrons, the current collection characteristics are calculated for each probe. The use of these current characteristics for the measurement of the electron temperature is discussed. A procedure is also given for obtaining the mean electron velocity perpendicular to the magnetic field in the case of a non-Maxwellian velocity distribution. Finally, methods for measuring the ion temperature are presented for the special case of a small Debye length compared with the ion Larmor radius.

scholarly journals Effect of electron temperature in a magnetized plasma sheath using kinetic trajectory simulation

BIBECHANA ◽  
2021 ◽  
Vol 18 (1) ◽  
pp. 58-66
Author(s):  
R Chalise ◽  
S K Pandit ◽  
G Thakur ◽  
R Khanal
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Electron Temperature ◽  
Electron Emission ◽  
Plasma Sheath ◽  
Magnetized Plasma ◽  
Total Charge ◽  
Ion Temperature ◽  
Trajectory Simulation ◽  
Total Charge Density

The understanding of the properties of magnetized plasma sheath has been various beneficial applications in surface treatment, electron emission gun, ion implantation, and nuclear fusion, etc. The effect of electron temperature on the magnetized plasma sheath has been studied for a fixed magnetic field and ion temperature. It has been observed that various plasma sheath parameters can be prominently altered by the varying temperature of the electron. The density of ion is influenced more by the change in electron temperature rather than the electron density. The temperature of the electron has a great effect at the wall, when electron temperature increases, the ion and electron densities at the wall decreases. This shows the potential at the wall also decreases follows the Poisson’s equation. Similarly, the electric field also decreases but total charge density increases when the electron temperature is increased. BIBECHANA 18 (2021) 58-66

scholarly journals Beat wave cyclotron heating of rippled density plasma

2018 ◽  
Vol 36 (4) ◽  
pp. 465-469 ◽  
Author(s):  
Pushplata ◽  
A. Vijay
Keyword(s):  
Magnetic Field ◽  
Large Amplitude ◽  
Ponderomotive Force ◽  
Beat Frequency ◽  
Magnetized Plasma ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Wave Heating ◽  
The Magnetic Field ◽  
Density Plasma

AbstractLaser beat wave heating of magnetized plasma via electron cyclotron damping is proposed and analyzed. A plasma density ripple is presumed to exist across the magnetic field. Two collinear lasers propagating along the magnetic field exert a beat frequency ponderomotive force on electrons, driving a large amplitude Bernstein quasi-mode which suffers cyclotron damping on electrons. Finite Larmor radius effects play an important role in the heating. Electron temperature initially rises linearly with time. As the temperature rises cyclotron damping becomes stronger and temperature rises rapidly. The process, however, requires ripple wavelength shorter than the wavelength of the beat wave.

scholarly journals Flow damping due to stochastization of the magnetic field

2015 ◽  
Vol 6 (1) ◽  
Author(s):  
K. Ida ◽  
◽  
M. Yoshinuma ◽  
H. Tsuchiya ◽  
T. Kobayashi ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Rational Surface ◽  
Magnetized Plasma ◽  
Ion Temperature ◽  
Flow Shear ◽  
Ion Temperature Gradient ◽  
Diffusive Term ◽  
Stochastic Magnetic Field ◽  
The Magnetic Field ◽  
Linear Decay

Abstract The driving and damping mechanism of plasma flow is an important issue because flow shear has a significant impact on turbulence in a plasma, which determines the transport in the magnetized plasma. Here we report clear evidence of the flow damping due to stochastization of the magnetic field. Abrupt damping of the toroidal flow associated with a transition from a nested magnetic flux surface to a stochastic magnetic field is observed when the magnetic shear at the rational surface decreases to 0.5 in the large helical device. This flow damping and resulting profile flattening are much stronger than expected from the Rechester–Rosenbluth model. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. This observation suggests that the flow damping is due to the change in the non-diffusive term of momentum transport.

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