Showing papers in "Plasma Physics in 1980"
TL;DR: In this paper, an extensive account is given of experiments in which an homogeneous preformed plasma of density 6*1016 cm-3 was heated by 10.6 mu m radiation focused on 1011 W cm-2.
Abstract: An extensive account is given of experiments in which an homogeneous preformed plasma of density 6*1016 cm-3 was heated by 10.6 mu m radiation focused on 1011 W cm-2. Ruby laser scattering gave space and time resolved measurements of the resultant density and temperature, showing large temperature gradients up to lambda e mod Delta T mod /T=0.5. Enhanced low frequency turbulence was observed. When compared with a one dimensional computer code, the observed temperature gradients imply that the heat flux was limited to 4+or-2% of the free streaming limit but that the absorption was 1.1+or-0.5 times the classical inverse bremsstrahlung absorption rate. The observed Te/Ti and lambda e mod Delta T mod /T were sufficient to excite heat flux driven ion acoustic turbulence, which explains the observed low frequency turbulence. This turbulence level is shown to be large enough to account for the observed thermal conductivity.
139 citations
TL;DR: For a toroidal plasma rotating about its axis of symmetry, the ideal MHD equations can be reduced to an equation which generalizes the static equilibrium equation if either the entropy or the temperature is constant on the magnetic surfaces.
Abstract: For a toroidal plasma rotating about its axis of symmetry, the ideal MHD equations can be reduced to an equation which generalizes the static equilibrium equation if either the entropy or the temperature is constant on the magnetic surfaces. For both of these cases, exact analytic solutions are obtained and their properties are discussed.
131 citations
TL;DR: In this paper, nonlinear reduced equations for stellarators were derived based on the standard low beta, large aspect ratio, epsilon 12/ϵ-12/ε.
Abstract: Nonlinear reduced equations are derived for stellarators, based on the standard low beta, large aspect ratio, epsilon 12/. Previous equations describing equilibrium and stability are recovered. The reduced equations make nonlinear hydromagnetic computations much more tractable.
96 citations
TL;DR: In this paper, the nonlinear evolution of the ion pressure gradient driven drift wave instability is investigated through three-dimensional fluid simulations, and anomalous thermal transport produced in the saturated state is reported as a function of the system parameters.
Abstract: The nonlinear evolution of the ion pressure gradient driven drift wave instability is investigated through three-dimensional fluid simulations. The anomalous thermal transport produced in the saturated state is reported as a function of the system parameters.
94 citations
TL;DR: In this article, a non-local cylindrical model is developed and solved numerically to yield dispersion characteristics which are compared with a local slab model dispersion relation, which is shown to be inadequate in describing how mode stability varies with azimuthal mode number.
Abstract: Experimental and theoretical results pertaining to the collisional drift instability of a weakly ionized plasma are presented. A non-local cylindrical model is developed and solved numerically to yield dispersion characteristics which are compared with a local slab model dispersion relation. The local slab model is shown to be inadequate in describing how mode stability varies with azimuthal mode number. Detailed experimental observations of single mode coherent oscillations in a weakly ionized argon plasma are also presented. The oscillations are identified as collisional drift waves on the basis of a comparison of mode characteristics with theory. Moreover, the experimental results demonstrate that the local slab model is a poor choice for describing these non-local cylindrical experiments.
79 citations
TL;DR: In this paper, the results of computer simulations of double layers are presented and scaling laws giving the dependence of the amplitude and width of the electric pulse on the potential difference between the two plasmas are given.
Abstract: Electric double layers provide a mechanism for the acceleration of particles. The results of computer simulations of double layers are presented. Simulations are carried out for the case of two interpenetrating plasmas with different plasma potentials. It is found that when the two plasmas satisfy the Langmuir condition for the existence of a double layer, stable double layers eventually form. During formation the initial constant electric field evolved in a solitary electric pulse of a constant shape. This pulse makes few oscillations before it becomes stationary. Scaling laws giving the dependence of the amplitude and width of the electric pulse on the potential difference between the two plasmas are given. When the Langmuir condition is not satisfied the double layer forms very swiftly and beam-plasma interactions on the high potential side of the layer cause strong instabilities, giving rise to strong RF fields which create an additional double layer through the action of a ponderomotive force.
67 citations
TL;DR: In this article, a modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping) and the possibility of including the ion dynamics in the analysis is also demonstrated.
Abstract: Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping) The possibility of including the ion dynamics in the analysis is also demonstrated As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important The relevance of this problem to laboratory experiments is discussed
59 citations
TL;DR: In this article, the authors studied the phenomenon of mode coupling in the discrete Alfven wave spectrum of ideal magnetohydrodynamics using a simplified plasma model and showed that mode coupling occurs when a periodic modulation of the equilibrium magnetic field strength and curvature is introduced, either by toroidicity or by noncircularity of the cross-section.
Abstract: The phenomenon of mode coupling in the discrete Alfven wave spectrum of ideal magnetohydrodynamics is studied using a simplified plasma model. It is shown that mode coupling occurs when a periodic modulation of the equilibrium magnetic field strength and curvature is introduced, either by toroidicity or by noncircularity of the cross-section. The existence of gaps in the frequency spectrum and the spatial localization of the eigenfunction as a result of mode coupling is analogous to the behavior of valence electrons in a one-dimensional crystal lattice.
55 citations
TL;DR: In this article, an analytic study of electrostatic and electromagnetic oscillations of an isotropic relativistic plasma is presented in order to correlate separate results obtained by different authors and to form a general qualitative picture of the oscillation branches of such a plasma.
Abstract: An analytic study of electrostatic and electromagnetic oscillations of an isotropic relativistic plasma is presented in order to correlate separate results obtained by different authors and to form a general qualitative picture of the oscillation branches of such a plasma. It is shown that at any plasma temperature there is only one dispersion curve of slightly damped (or undamped) electrostatic oscillations. Separate parts of this dispersion curve are, however, described by different analytic formulas depending on the plasma temperature and the ratio of the phase velocity to the characteristic velocity of the particles. Considerable attention is given to the study of the dispersion of subluminous electrostatic waves and their damping since such waves may be responsible for the electrostatic beam instabilities. It is concluded that there are two kinds of electromagnetic oscillations, i.e. normal superluminous nondamping and subluminous aperiodically damping oscillations.
44 citations
TL;DR: In this paper, the properties of the Alfven surface wave along a cylindrical plasma column surrounded by vacuum or by another plasma medium are discussed, and both symmetric and asymmetric modes are found to be dispersive in nature.
Abstract: The properties of Alfven surface waves along a cylindrical plasma column surrounded by vacuum or by another plasma medium are discussed. Both symmetric (m=0) and asymmetric (m=+or-1) modes are found to be dispersive in nature. The interfacial symmetric modes propagate in a certain frequency window ( omega A1, omega As), where omega As is the Alfven surface wave frequency along the interface of two semi-infinite media; when nu A1> nu A2 these modes propagate as backward waves and when nu A1 nu A2.
43 citations
TL;DR: In this article, a Fokker-Planck treatment of the effect of trapped electrons on the current induced by a beam of fast ions circulating in a toroidal plasma is presented.
Abstract: A Fokker-Planck treatment of the effect of trapped electrons on the current induced by a beam of fast ions circulating in a toroidal plasma is presented. The theory applies to the 'banana' regime of small collision frequency and to systems of large aspect ratio. The perturbation of the electron distribution function due to trapping is described by an integro-differential equation in which the driving term depends on the electron distribution function for no trapped electrons. This equation is solved (a) analytically for a large plasma Zeff and (b) numerically for several values of Zeff and for the complete range of ve/vb, the ratio of the electron thermal and fast ion velocities. The effect of trapped electrons on the current driven by the toroidal rotation of the thermal ions is also discussed. The net circulating current predicted by the theory is presented for parameters relevant to present and planned Tokamak experiments.
TL;DR: In this article, an 85 kV/12 kJ device with a current rise time of 600 ns was investigated and the obtained neutron yield was larger by a factor of 3 compared to devices of equal energy but low voltage.
Abstract: Numerical and experimental studies have been made concerning an increase of the effective discharge current for the plasma focus from a bank of constant energy. From the higher discharge current an increased neutron yield is expected. Experimentally an 85 kV/12 kJ device with a current rise time of 600 ns was investigated. The obtained neutron yield was larger by a factor of 3 compared to devices of equal energy but low voltage. The geometrical and pressure variations necessary for optimization, are discussed. Using MHD-calculations and impedance considerations, various banks, including those with high voltage and low inductance, are compared with respect to plasma data and discharge current.
TL;DR: In this article, a general method for investigating stability of low-frequency electrostatic oscillations of magnetically confined plasma, which was developed in Part I (1968) for equilibria with closed field lines (e.g. multipoles), is extended to axisymmetric toroidal equilibrium with finite magnetic shear, and the determination of stability is reduced to a single one dimensional integro-differential equation-which must be solved numerically for each given equilibrium.
Abstract: For pt.II see ibid., vol.23, p.265 (1971). A general method for investigating stability of low-frequency electrostatic oscillations of magnetically confined plasma, which was developed in Part I (1968) for equilibria with closed field lines (e.g. multipoles), is extended to axisymmetric toroidal equilibria with finite magnetic shear (e.g. Tokamaks). The analysis encompasses all perturbations whose parallel wavelengths are comparable to equilibrium scale lengths and whose perpendicular wavelengths are comparable to ion Larmor radii. Once the problem of reconciling these characteristics with toroidal periodicity has been overcome, the investigation of any axisymmetric toroidal equilibrium becomes very similar to that of closed line equilibria and the ion and electron charge densities resulting from an arbitrary potential perturbation are calculated by a small Larmor radius expansion as in Part I. Using these expressions the determination of stability is reduced to a single one dimensional integro-differential equation-which must be solved numerically for each given equilibrium. In the most general case this requires considerable computation, but in many circumstances one can use simpler approximate forms of this equation which are also derived.
TL;DR: In this paper, the authors measured the ion kinetic energies up to approximately 40 keV at a large range of distances from the target (8 mm to 2.18 m) for a laser-produced plasma created by a neodymium laser of pulse length 4 ns focused to an intensity approximately 1016 Wm-2 onto a solid carbon slab.
Abstract: Ion kinetic energies up to approximately=40 keV measured at a large range of distances from the target (8 mm to 2.18 m) for a laser-produced plasma created by a neodymium laser of pulse length 4 ns focused to an intensity approximately 1016 Wm-2 onto a solid carbon slab are presented. With increasing distance from the target, an increase in average ion energy and a decrease in the number of ions detected for each ion species is observed up to a distance of 1.45 m from the target, while at longer distances (>1.45 m) the average ion energy and number of ions detected remain approximately constant with increasing distance from the target. The results show that recombination is important in determining the ion energy spectra observed in laser-produced plasma studies, but that there are also (higher energy) ions which are 'frozen' in high charge states and do not recombine even by the time they have travelled long distances from the target.
TL;DR: In this paper, a modified K-dV equation was used to give damped or growing solitons with tail formation on the reverse side of a collisionless plasma, and it was shown that for a given soliton width, the rates of these processes increase as the angle between the propagation vector and the magnetic field decreases.
Abstract: Nonlinear, finite amplitude electron-acoustic waves in a current carrying magnetized collisionless plasma, with ion temperature much greater than the electron temperature are found to be governed by a modified K-dV equation. Using the method of inverse scattering, it is shown that this equation gives damped or growing solitons with tail formation on the reverse side. For a given soliton-width, the rates of these processes increase as the angle between the propagation vector and the magnetic field decreases. But a change in the electron to ion temperature ratio affects only the velocity of the soliton.
TL;DR: In this article, the authors considered direct subharmonic wave generation in a non-uniform plasma and derived an expression for the instability growth rate, which includes collisions, resonance absorption and leaking losses.
Abstract: Direct subharmonic wave generation in a nonuniform plasma is considered. That mechanism exists only when leaking surface waves can be parametrically excited. An expression for the instability growth rate, which includes collisions, resonance absorption and leaking losses is derived. A possibility of generating subharmonics at omega 0/4, 3 omega 0/4 and 5 omega 0/4, where omega 0 is the pump wave frequency is pointed out, and the corresponding field intensities are estimated. The conditions for total energy absorption are discussed and the pump wave intensity, which produces complete absorption, is obtained for a plasma with a steep density gradient.
TL;DR: In this paper, the anomalous transport of particles and energy due to drift wave fluctuations in high temperature plasmas is derived and shown to lead to a positive definite form for the rate of internal entropy production.
Abstract: The anomalous transport of particles and energy due to drift wave fluctuations in high temperature plasmas is derived and shown to lead to a positive definite form for the rate of internal entropy production. The entropy production functional is the Lyapunov function for the thermodynamic system and is used to investigate the thermal stability of the steady state transport.
TL;DR: In this paper, a collisionless plasma whose ion energy distribution is controlled before entering into the mirror configuration is investigated, and the results are well explained by the orbit theory, and when the plasma density is so high that the ion-ion collision mean free path is comparable to the mirror length, a clear plasma trapping is observed.
Abstract: Particle reflection and trapping are investigated on plasma flows injected into mirror-configurations of magnetic field. Detailed measurements are made on a collisionless plasma whose ion energy distribution is controlled before entering into the mirror configuration, and the results are well explained by the orbit theory. When the plasma density is so high that the ion-ion collision mean free path is comparable to the mirror length, a clear plasma trapping due to the collisions is observed. An instability around the ion-cyclotron frequency is excited in order to trap a collisionless plasma, and enhanced tail heating of ion energy distribution is observed in addition to the trapping.
TL;DR: In this article, the authors suggest that the fast ions, which are presumably produced in the collapsing phase, are actually confined for a substantial length of time within the focus region, before being lost to the electrodes.
Abstract: It appears difficult to account for the large number of neutrons produced per shot in plasma foci, as well as for the long duration of the neutron emission phase, unless one assumes that the fast ions, which are presumably produced in the collapsing phase, are actually confined for a substantial length of time within the focus region, before being lost to the electrodes. The authors suggest that such a confinement may be provided by the mirror properties of the quasi force-free, helical configurations, which were predicted by Taylor (1976) to be the likely end point for highly-sheared, dissipative pinch discharges. In fact, in plasma foci, particularly of the Filippov type, evidence has accumulated in favor of the existence of long lasting ( approximately 100 nsec) helical plasma-magnetic structures, which seem to occur simultaneously with the second neutron outburst (Rager, 1976).
TL;DR: In this article, the effect of ion beam velocity, beam ion density and plasma ion to beam ion mass ration on the amplitude and width of ion acoustic solitons has been investigated.
Abstract: Reductive perturbation method has been employed to obtain a modified KdV equation and to show the excitation of ion acoustic solitons in an ion beam-plasma system consisting of bulk of cold ions, beam ions and non-isothermal and resonant electrons (both trapped and free electrons). The effect of ion beam velocity, beam ion density and plasma ion to beam ion mass ration on the amplitude and width of ion acoustic solitons has been investigated. The beam amplification rate of solitons amplitude is found to depend upon the ion beam velocity. There exists a critical ion beam velocity below which the ion beam is unable to generate solitons and this threshold ion beam velocity is an increasing function of the ion beam concentration and the mass ratio of background plasma ions and beam ions.
TL;DR: In this paper, the effect of a small fraction of superthermal electrons on the absorption of the extraordinary mode near the cyclotron resonance and on the emission of radiation near the second harmonic is investigated.
Abstract: The effect of a small fraction of superthermal electrons on the absorption of the extraordinary mode near the cyclotron resonance and on the emission of radiation near the second harmonic is investigated. It is shown that the use of the extraordinary mode for electron cyclotron plasma heating may result in the acceleration of a small fraction of the electron population. It is also shown that the emission of radiation at the second harmonic from a tenuous plasma with reflecting boundaries is critically dependent on the presence of the superthermal electrons.
TL;DR: In this paper, an energy principle for "helical" incompressible perturbations in shaped cross-section plasmas is derived in the Tokamak scaling (epsilon identical to ka approximately=Bperpendicular to /Bz<<1).
Abstract: An energy principle for 'helical' incompressible perturbations in shaped cross-section plasmas is derived in the Tokamak scaling ( epsilon identical to ka approximately=Bperpendicular to /Bz<<1). Two models for the resistivity are used. The resistivity is assumed to be transported either by the fluid or by the magnetic surfaces. In the first case generalized rippling and tearing modes are discovered, while in the latter case the rippling is cancelled in a self-consistent way. The Euler equation for the tearing modes generalizes the previously derived equation for two-dimensional perturbations. It is pointed out that the energy principle cannot be extended to higher orders in epsilon .
TL;DR: In this paper, the influence of ion motion in the lower hybrid domain is pointed out and the shift of the resonance cone angle in a drifting plasma is investigated using an RF double probe technique.
Abstract: Resonance cones are studied in a wide range of plasma parameters using an RF double probe technique. Particularly, the influence of ion motion in the lower hybrid domain is pointed out. In addition, the shift of the resonance cone angle in a drifting plasma is investigated.
TL;DR: In this paper, the component of the magnetic vector potential in the direction of an ignorable coordinate of the field geometry can be determined by measuring the velocity of beam particles that undergo ionizing collisions in the plasma.
Abstract: Diagnostic systems based on the injection of particle beams into hot, dense plasmas are shown to be directly sensitive to confining magnetic fields. In particular, the component of the magnetic vector potential in the direction of an ignorable coordinate of the field geometry can be determined by measuring the velocity of beam particles that undergo ionizing collisions in the plasma.
TL;DR: In this article, the spectral structure of turbulence in a plasma confined by a strong homogeneous magnetic field was investigated by means of a fluid description, and the turbulent spectrum was divided into subranges.
Abstract: An investigation of the spectral structure of turbulence in a plasma confined by a strong homogeneous magnetic field was made by means of a fluid description. The turbulent spectrum is divided into subranges. Mean gradients of velocity and density excite turbulent motions, and govern the production subrange. The spectra of velocity and potential fluctuations interact in the coupling subrange, and the energy is transferred along the spectrum in the inertia subrange. Applying the method of cascade decomposition, the spectral laws k-3, k-3, k-2 are obtained for the velocity fluctuations, and k-3, k-5, k-3/2 for the potential fluctuations in the production, coupling and inertia subranges, respectively. The coefficient of Bohm diffusion is reproduced, and its role in electrostatic coupling is derived. Comparison is made with measured power laws reported in the literature, from Q-devices, hot-cathode reflex arc, Stellarator, Zeta discharge, ionospheric plasmas, and auroral plasma turbulence.
TL;DR: In this paper, it is proposed that the fluctuation of the Zeta plasma is a byproduct of resistive instabilities through their action in cross-connecting lines of force belonging to magnetic surfaces at different radii.
Abstract: An outstanding problem in the behaviour of the Zeta plasma is the origin of the fluctuations of density; it has been shown experimentally that they do not arise directly from the observed turbulent motions of the plasma, and there is no known instability which can produce them directly. It is proposed that they arise as a by-product of resistive instabilities through their action in cross-connecting lines of force belonging to magnetic surfaces at different radii. This idea is developed quantitatively and it is shown that it predicts fluctuation levels in reasonable agreement with experiment. This result is interpreted as giving support to the tangled discharge model of the Zeta plasma.
TL;DR: In this paper, the nonlinear decay of the electrostatic daughter wave was shown to provide an efficient saturation mechanism for stimulated Brillouin and Raman scattering, and the saturation effect due to the Langmuir decay is even stronger.
Abstract: The nonlinear decay of the electrostatic daughter wave is shown to provide an efficient saturation mechanism for stimulated Brillouin and Raman scattering. The saturated steady-state reflectivity due to SBS depends on the plasma density. In the range n or approximately=0.25 ncr. In the stimulated Raman scattering the saturation effect due to the Langmuir decay is even stronger. SRS saturates to the value of the order of (ve/c)4 depending on the plasma temperature only. The effect of the ES daughter wave decay on the parametric decay instability is studied briefly. According to a rough analysis it seems likely that the secondary decay processes have only a small influence on the anomalous absorption near the critical density.
TL;DR: In this paper, the authors investigated the effect of deviation from strictly parallel propagation on the tunnelling of obliquely propagating extraordinary wave in plasmas whose parameters vary along the magnetic field (parallel stratification).
Abstract: The process of Budden tunnelling of obliquely propagating extraordinary model is investigated in plasmas whose parameters vary along the magnetic field (parallel stratification). The wave tunnels through the evanescent region separating the right-hand cutoff layer from the electron cyclotron resonance. Coupled mode equations describing both ordinary and extraordinary waves are drove for arbitrary angle of incidence with respect to the magnetic field. Under appropriate conditions (nx and d In(B)/dx not too large) the coupling can be ignored, and the usual Whittaker equation is obtained for a linear magnetic field profile. It is shown that deviation from strictly parallel propagation (nx not=0) has a very small effect on tunnelling for a wide range of angle of incidence. The analytical results are verified by numerical integration of the field equations. The theory is applied to the propagation of extraordinary mode waves in the surface plasma of the ELMO Bumpy Torus devices. Fractions of incident power absorbed and transmitted to the high field region in the range of 2-15% occur for a broad spectrum of nx.
TL;DR: In this article, the authors evaluate the forces for oblique incidence with collisions and find an absorption caused force in the plane of the plasma surface, while the first order terms of the derivations are remaining unchanged, new third order terms are found for the case of perpendicular incidence without collisions.
Abstract: The evaluation of the general expression of the nonlinear force of laser-plasma interaction showed discrepancies depending on the assumptions of the phase and collisions in the expressions used for E and H. While the first order terms of the derivations are remaining unchanged, new third order terms are found for the case of perpendicular incidence without collisions. With collisions, the additional nonponderomotive terms are derived to be more general than known before. The authors are then able to evaluate the forces for oblique incidence with collisions and find an absorption caused force in the plane of the plasma surface.
TL;DR: In this article, it was shown analytically that the presence of dissipative processes limits the propagation coefficient of a plasma wave propagating along a plasma cylinder and that the main dipole and multiple resonances are limits of the mode of the wave.
Abstract: It is shown analytically that the presence of dissipative processes limits the propagation coefficient of guided electron plasma waves propagating along a plasma cylinder and that the main dipole and multiple resonances are limits of respective mode of guided electron plasma waves.