Collisional Limit Research Articles

Investigation of the Paschen curve of nitrogen via the application of nanosecond pulsed electromagnetic radiation

The Paschen curve of nitrogen from pressures of 0.336 to 685 Torr via the application of nanosecond pulsed electromagnetic radiation has been investigated. Breakdown of the gas was achieved via pumping by short electromagnetic pulses and verified through the use of an optical multichannel analyzer. Adjustments for the short pulse nature of this investigation have been derived and are applied to the Paschen curve. The experiments were conducted utilizing a pulser with machine parameters of 1 J delivered during 1.375 ns FWHM into a 50 Ω coaxial line, at a peak power of 1 GW. Investigation of this region has yielded data in the region of the relativistic Paschen curve as hypothesized by Graham and Roussel-Dupré. Experimental results yield no observable relativistic effects under the conditions of this experiment. Additionally, the collisional frequency limit has been experimentally identified.

Analytic expressions for mode conversion in a plasma at the peak of a parabolic density profile

For mode conversion in an unmagnetized plasma with a parabolic density profile of scale length L, analytic expressions, in terms of parabolic cylinder functions, for the energy flux coefficients (reflection, transmission, and mode conversion) and the fields for both the ‘‘direct’’ problem (incident electromagnetic wave converting to a Langmuir wave) and the ‘‘inverse’’ problem (incident Langmuir wave converting to an electromagnetic wave) are derived for the case where the incident wave frequency ω matches the electron plasma frequency ωp at the peak of the density profile. The mode conversion coefficient for the direct problem is equal in magnitude to that of the inverse problem, and the corresponding reflection and transmission coefficients satisfy energy conservation. In contrast to the linear profile problem, the conversion efficiency depends explicitly on the value of the collision frequency (in the cold, collisional limit) or electron temperature (in the warm, collisionless limit), but a transformation of parameters relates the results for these two limits.

Short scale radiative condensation instabilities in tokamak edge plasma

The linear evolution of radiative condensation driven short scale fluctuations has been studied using the ballooning mode formalism. A non-uniform plasma is considered with ion transport in the Pfirsch-Schluter regime and electrons in the anomalous regime. The perpendicular thermal conductivities are taken to be poloidally asymmetric, i.e. χ⊥0 (1 + Δcos θ), where θ is the poloidal angle. For typical values of Δ ⩾ 0.5, the fluctuations are found to be localized on the inboard side of tokamaks. In the collisional limit (me/mi) νei >> ω, the curvature does not affect the growth rate. Anomalous diffusion is found to reduce the critical poloidal mode number

Neoclassical viscosity effects on resistive magnetohydrodynamic modes in toroidal geometry

The flux-surface-averaged linearized resistive magnetohydrodynamic (MHD) boundary-layer equations including the compressibility, diamagnetic drift, and neoclassical viscosity terms are derived in toroidal geometry. These equations describe the resistive layer dynamics of resistive MHD modes over the collisionality regime between the banana plateau and the Pfirsch–Schlüter. From the resulting equations, the effects of neoclassical viscosity on the stability of the tearing and resistive ballooning modes are investigated numerically. Also, a study is given for the problem of how the neoclassical resistive MHD mode is generated as the collisionality is reduced. It is shown that the neoclassical viscosity terms give a significant destabilizing effect for the tearing and resistive ballooning modes. This destabilization comes mainly from the reduction of the stabilizing effect of the parallel ion sound compression by the ion neoclassical viscosity. In the banana-plateau collisionality limit, where the compressibility is negligible, the dispersion relations of the tearing and resistive ballooning modes reduce to the same form, with the threshold value of the driving force given by Δc=0. On the other hand, with the finite neoclassical effect it is found that the neoclassical resistive MHD instability is generated in agreement with previous results. Furthermore, it is shown that this later instability can be generated in a wide range of the collisionality including near the Pfirsch–Schlüter regime as well as the banana-plateau regime, suggesting that this mode is a probable cause of anomalous transport.

K-P Burgers Equation for the Decayof Solitary Magnetosonic Waves Propagating Obliquelyin a Warm Collisional Plasma

A nonlinear evolution equation governing the two dimensional propagation of fast and slow magnetosonic modes in a warm collisional plasma has been derived. This equation is a combination of Kadomtsev-Petviashvili (K-P) equation and the Burgers equation. The two dimensional K-P equation has two types of solitary wave solutions depending on the sign of the coefficients. One type is the usual planar type, the other is the lump solution. Both types of solitary wave solutions decay with time in the weak collisional limit. The two dimensional features of the amplitude and width of the lump or algebraic soliton have been discussed and the decay rates computed numerically. The decay rates depend on plasma beta and on the angle of propagation and the rates are different for the fast and the slow waves. At a certain angle of propagation the decay rates of both the modes are equal in the case of low beta plasma. Because of 2-D effects, the slow mode, although it has a lower collisional decay rate than the fast mode,...

Simulation of high‐speed (orbital) releases of electron attachment materials in the ionosphere

The dynamics of ionospheric plasma irregularities produced by the release of electron attachment materials at orbital velocities across the geomagnetic field is studied. A two‐dimensional electrostatic fluid model which includes electron attachment and mutual neutralization chemistry, self‐consistent electric fields, and three‐species transport is developed. Numerical simulations are performed to study the behavior at early and at late times after the release. At early times, of the order of or less than the attachment material neutral collision time, the negative ion cloud produced by the release may structure owing to the shear in the E×B velocity within the cloud. At high altitudes the cloud may bifurcate and form vortices on the back. At lower altitudes where ion‐neutral collisional effects dominate, this structuring is suppressed. At late times, after a plasma depletion has formed due to neutralization chemistry, the cloud structures by the E×B interchange instability. Depending on the release altitude, the depletion structures by the collisional or inertial limit of this instability.

Effective plasma heat conductivity in 'braided' magnetic field-II. Percolation limit

For pt.I see ibid., vol.33, no.7, p.795-807 (1991). This paper is devoted to the problem of anomalous transport across a magnetic field that includes a small stochastic component delta B. The perturbation is assumed to be so strongly stretched along the background magnetic field B0 that the parameter R is large: R identical to b0L0/ delta >>1 (here b0 identical to delta Bperpendicular to /B0<<1, and L0 is the longitudinal and delta the transverse correlation length of the magnetic perturbation). This strong turbulence limit, which is opposite to the quasi-linear one (R<<1), has certain notable features. The principal result is that the main transport is concentrated in very thin regions, being fractal sets with the dimension df, which can range in value from 2 to 2.75, depending on the spectrum of the magnetic perturbation. These regions consist of a small fraction of magnetic lines that percolate, that is, walk from the nonperturbed magnetic flux surfaces to a distance large compared to the transverse correlation length delta . Due to such a strong inhomogeneity of the transport distribution, as well as the long correlations, the standard transport averaging techniques fail, and one should make use of the percolation theory methods. Thus the strong turbulence regime is referred to here as the percolation limit. In comparison with the quasi-linear limit, the percolation limit has several additional intermediate regimes and the expressions for the effective heat conductivity chi eff include the critical exponents of 2-D percolation theory. The estimates of chi eff are obtained both in the collisional and collisionless limits, including the case of nonstationary magnetic perturbations.

Effective plasma heat conductivity in 'braided' magnetic field-I. Quasi-linear limit

Anomalous cross-field electron transport in a specified magnetic field with weakly-destroyed flux surfaces is discussed. Following the approach developed previously in the present paper the regimes of effective transverse plasma transport are studied systematically, both in the collisional and collisionless limits. The present analysis incorporates the nonstationary of magnetic perturbations, which was not included in the previous works. Part I of this study deals with the quasi-linear approximation, which may be written as b0L0/ delta <<1, where b0= delta Bperpendicular to /B0 represents the relative magnitude of the transverse magnetic perturbation, while L0 and delta represent the longitudinal and transverse correlation lengths, respectively. It is found that some of the previously-described transport regimes cannot be considered as anomalous (in the sense that effective heat conduction chi eff>> chi perpendicular to ) for time-independent magnetic perturbations. However, these regimes can exist in the presence a finite-frequency magnetic flutter. A unified classification of quasi-linear regimes of anomalous transport is introduced in order to further extend the analysis to the strong magnetic turbulence limit b0L0/ delta >>1 (see Part II), which is considered as a companion paper. (Isichenko, ibid., vol.33, no.7, p.809-26 (1991)).

A fluid treatment of the plasma presheath for collisionless and collisional plasmas

The presheath region of an unmagnetized plasma is treated using ion fluid equations in the collisional and collisionless regimes. Effects of neutral gas–plasma interactions are included through source terms in the fluid equations. Ion–ion collisional effects are included through the closure conditions of the fluid equations. In the collisionless regime, the perpendicular ion temperature is assumed constant and independent of the parallel ion temperature. In the collisional limit, the parallel and perpendicular temperatures are assumed equal throughout the presheath. Profiles of ion density, flow velocity, parallel temperature, and energy flux obtained by integrating the fluid equations compare well to previously published kinetic results in the collisionless case. Ion–ion Coulomb collisions are shown to have a negligible effect on the ion particle and energy flux into the sheath.

Generalized parallel heat transport equations in collisional to weakly collisional plasmas

A new set of two-fluid heat transport equations that is valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates, a set of moment equations describing plasma energy transport along the field lines of a space- and time-dependent magnetic field is derived. No restrictions on the anisotropy of the ion distribution function or collisionality are imposed. In the highly collisional limit, these equations reduce to the classical heat conduction equation (e.g., Spitzer and Härm or Braginskii), while in the weakly collisional limit, they describe a saturated heat flux (flux limited). Numerical examples comparing these equations with conventional heat transport equations show that in the limit where the ratio of the mean free path λ to the scale length of the temperature gradient LT approaches zero, there is no significant difference between the solutions of the new and conventional heat transport equations. As λ/LT→1, the conventional heat conduction equation contains a significantly larger error than (λ/LT)2. The error is found to be O(λ/L)2, where L is the smallest of the scale lengths of the gradient in the magnetic field, or the macroscopic plasma parameters (e.g., velocity scale length, temperature scale length, and density scale length). The accuracy of the flux-limited model depends significantly on the value of the flux limit parameter which, in general, is not known. The new set of equations shows that the flux-limited parameter is a function of the magnetic field and plasma parameter profiles.

The collisional limit: an important consideration for membrane-associated enzymes and receptors.

Because of the proximity of many bound receptors or enzymes, a membrane surface may become uniformly reactive so that every collision between a ligand and the membrane particle results in a binding or catalytic event. At this limit (the collisional limit), the reaction rate depends on membrane particle (cell) concentration and is independent of receptor concentration. Many receptor systems display properties that satisfy the requirements of a collisionally limited reaction. These include the presence of many receptors per cell. The filling of only a few of these receptors often generates the maximum cellular response, and the remaining receptors have been referred to as spare receptors. However, many receptors are needed to produce the collisional limit, and spare receptors may represent nature's evolution toward a reaction that provides the maximum rate as well as the maximum sensitivity to a ligand. Since receptors or enzymes provided on small membrane fragments will not function at the collisional limit, properties of reconstituted enzymes or receptors may not be extrapolated to the physiological situation. The use of normal bimolecular kinetic or equilibrium equations is inappropriate for reactions limited by collision and can give unusual results that lead to inappropriate conclusions. Determination of whether the collisional limit applies to a membrane-bound system is important for understanding its properties and those of the physiological circumstance.

Marginal stability of ion-acoustic waves in a weakly collisional two-temperature plasma without a current.

Abstract : This report presents two important results for a weakly collisional, current-free, two-temperature electron-ion plasma: (1) that e-i collisions have an undamping effect on ion acoustic waves, and (2) that, for appropriate values of the plasma parameters, ion-acoustic waves become marginally stable. The results are based on the closed form solution for the dielectric function for the linearized Balescu-Lenard-Poisson kinetic equations. The weakly collisional ordering is necessary to obtain an iterative solution for the collisional dielectric function, imposes two independent restrictions on the parameters that characterize the plasma. The linearized Balescu-Lenard-Poisson equations are solved in the weakly collisional limit to show that ion-acoustic waves in a current-free plasma, which are Landau-damped in the absence of collisions, can become marginally stable due to the undamping effect of electron-ion (e-i) collisions. For sq rt.(T sub e0/T sub i0) (5/16) sq rt.(m sub i/m sub e), the e-i collisional undamping effect dominates the i-i, e-e, and i-e collisional effects, and marginal stability occurs when the collisional undamping rate balances the electron and ion Landau damping rates. Keywords: Ion acoustic waves; Two temperature plasma. (JHD)

Problems with non-thermal models for the narrow line gamma rays reported from SS 433

The jet/grain model proposed by Ramatyet al. (1984, hereafter abbreviated as RKL) for production of the narrow gamma-ray lines reported from SS433 is examined and shown to be untenable on numerous grounds. Most importantly: (a) The huge Coulomb collisional losses (Wc≳2×1041 erg s−1) from the jet, which would necessarily accompany non-thermal production of the gamma rays, demands a jet acceleration/collimation process acting over a very long range and with a power at least 102 times the Eddington limit for any stellar object. (b) There is a collisional thick target limit (irrespective of jet mass) to the gamma ray yield per interstellar proton. Consequently, the gamma-ray data demand an improbably high interstellar density (≳109 cm−3). (c) For the grains to be kept cool enough (≲3000 K) to survive the heating rateWc either by radiation or jet expansion would demand a ‘jet’ wider than its length and so inconsistent with narrow lines. In the case of radiative cooling, the resultant IR flux would exceed the observed values by a factor ≳104. (d) Light scattered on the jet grain mass required would be highly polarized, contrary to observations, unless the jet was optically thick to grains, again precluding their radiative cooling. (e) To avoid unacceptable precessional broadening of the gamma-ray lines demands an emitting jet length ≲0.5 days atv=0.26c. This increases the necessary mass loss rate by a factor ≅10 over the values obtained by RKL who assumed a 4-day ‘flare’. (f) The model also predicts rest energy gamma-ray lines which are not observed.

Association of a protein with membrane vesicles at the collisional limit: studies with blood coagulation factor Va light chain also suggest major differences between small and large unilamellar vesicles.

Vesicle size can be a very sensitive modulator of protein-membrane association. In addition, reactions at the collisional limit may be characteristic of many types of protein-membrane or protein-receptor interactions. To probe these effects quantitatively, we analyzed the association of blood clotting factor Va light chain (Va-LC) with phospholipid vesicles of 15-150-nm radius. The number of protein binding sites per vesicle was approximately proportional to vesicle surface area. Association rates approached the collisional limit, and the activation energy for the association reaction was 4.5 +/- 0.5 kcal/mol. In agreement with diffusional theory for this type of interaction at the collisional limit, the observed association rate constant for filling all sites was approximately proportional to the inverse of vesicle radius. This general property has important implications for many systems such as blood coagulation including possible slower association rates and higher Km values for reactions involving whole cells relative to those obtained for phospholipid vesicles. Dissociation rate constants for reactions that are near the collisional limit should also be proportional to the inverse of vesicle size if diffusional parameters are the only factors influencing dissociation. However, Va-LC bound to small unilamellar vesicles (SUVs, less than or equal to 15-nm radius) gave slower dissociation rates than Va-LC bound to large unilamellar vesicles (LUVs, greater than or equal to 35-nm radius). This indicated a change in KI, the intrinsic protein-phospholipid affinity constant for LUVs vs SUVs. The cumulative effect of association and dissociation rates resulted in higher affinity of Va-LC for SUVs than LUVs under equilibrium conditions. The latter was corroborated by competition binding studies. Furthermore, the temperature dependence of both rate constants indicated an entirely entropy-driven binding to LUVs but a largely enthalpy-driven binding to SUVs. Interactions which are largely entropic are thought to be ionic in nature. The differences observed between binding to LUVs and SUVs may reflect thermodynamic differences between these types of phospholipid structures.

Transverse Kelvin‐Helmholtz instability with parallel electron dynamics and Coulomb collisions

Electron parallel dynamics and Coulomb collisions are included in the analysis of the transverse Kelvin‐Helmholtz instability. The electrons are treated kinetically while the ions are treated in the fluid limit. It is shown that in the collisionless case, for an inhomogeneous velocity profile V(x) = V0 tanh (x/L) the Kelvin‐Helmholtz instability is stable for kz/ky &gt; (V0/Lωlh)kyL [2(1 ‐ ky²L²)]1/2 in the limit ω ‐ kyV0 » kzυe. Here V0 is the flow velocity, L is the scale length of the velocity shear layer, kz and ky are the parallel and perpendicular wave numbers, respectively, ωlh = (ΩeΩi)1/2, and υe is the electron thermal velocity. The stabilization of the mode is shown to be caused by the compressional energy given to the electrons parallel to B. In the collisional limit, Coulomb collisions are shown to increase the unstable kz domain because they inhibit the electron motion parallel to B. Applications to the high‐latitude ionosphere are discussed.

Quasi-steady-state current drive with pulsed radiofrequency sources

The problem of driving quasi-steady-state currents in tokamak plasmas with pulsed RF sources is examined in the regime , where τRF is the length of the RF pulse, is the electron collision time, TRF is the period between RF pulses, and TL/R is the L over R time of the tokamak plasma. This regime is appropriate to the proposed Microwave Tokamak Experiment (MTX) in which a pulsed free electron laser will be used to drive current in Alcator C. It is found that δI/Ī ≈ TRF/TL/R ≪ 1, where δI/Ī is the fractional variation in the plasma current. The production of runaway electrons can be a problem in the collisional limit, νe TRF ≫ 1. This will be avoided in the proposed MTX experiment if the electron temperature exceeds 1.5 keV.

Nonlinear evolution of drift instabilities in the presence of collisions

Nonlinear evolution of drift instabilities in the presence of electron–ion collisions in a shear-free slab has been studied by using gyrokinetic particle simulation techniques as well as by solving, both numerically and analytically, model mode-coupling equations. The purpose of the investigation is to determine the mechanisms responsible for the nonlinear saturation of the instability and for the ensuing steady-state transport. Such an insight is very valuable for understanding drift-wave problems in more complicated geometries. The results indicate that the electron E×B convection is the dominant mechanism for saturation. It is also found that the saturation amplitude and the associated quasilinear diffusion are greatly enhanced over their collisionless values as a result of weak collisions. In the highly collisional (fluid) limit, there is an upper bound for saturation with eφ/Te≂(ωl/Ωi)/(k⊥ ρs)2. The associated quasilinear diffusion, which increases with collisionality, takes the form of Dql≂γl/k2⊥, where ωl and γl are the linear frequency and growth rate, respectively. In the steady state, the diffusion process becomes stochastic in nature. The relevant mechanisms here are related to the velocity-space nonlinearities and background fluctuations. The magnitude of the diffusion at this stage can be comparable to that of quasilinear diffusion in the presence of collisions, and it seems to remain finite even in the collisionless limit.

Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas

A new set of two-fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero-order drifts, a set of moment equations describing plasma transport along the field lines of a space- and time-dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 236, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path λ to the scale length of the magnetic field gradient LB approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (λ/LB)2, are found to have errors of order (λ/Lu)2 =(λ/LB)2/(1−M2)2, where Lu is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (M≊1).

Effects of finite current channel width on the current convective instability

The effects of the finite current channel width on the current convective instability are studied both analytically and numerically. First, using a sharp boundary field‐aligned current distribution which has a finite width along the plasma density gradient, the dispersion relation is obtained analytically. It is found that for the long wavelength modes (kyd ≪ 1) where the nonlocal effects are most prominent, the growth rate γ is proportional to in the collisional limit (νin ≫ |ω|), where d is the half width of the current channel, L is the plasma density gradient scale length, is the field‐aligned current velocity, νin is the ion‐neutral collision frequency, and ω is the perturbation frequency. For the long wavelength modes in the inertial limit (νin ≪ |ω|) the growth rate γ scales as , where α = 1/2 (2/3) for kz²/ky² Ωe/νei much less than (greater than) |ω|/Ωi, kz(ky) is the wave number parallel (perpendicular) to the magnetic field, Ωe(Ωi) is the electron (ion) gyrofrequency, and νei is the electron‐ion collision frequency. Numerical results are also presented for a diffuse boundary current velocity distribution. Applications to the high‐latitude ionosphere are discussed.

Striation eigenmodes along the geomagnetic field and eigenvalues in the limit of strong ion‐neutral collisions

A second‐order linear differential equation is derived for determining the linear eigenmodes of striation instabilities along the geomagnetic field. Eigenvalues (i.e., temporal frequencies in complex space) are determined along with the eigenmodes. The differential equation includes the contribution of two significant physical effects, ion polarization currents and inductive electric fields. The numerical evaluation of the differential equation emphasizes the collisional limit appropriate to situations when the instabilities are driven at altitudes where the ion‐neutral collision frequency is much larger than the growth rate for the instability. The numerical results indicate that the instabilities can drive parallel electron currents in the magnetosphere. However, because of finite parallel resistivity, magnetic field lines generally cannot be considered to be equipotentials. It is suggested that the coefficient for ion diffusion resulting from ion‐neutral collisions plays an important role in determining the maximum perpendicular wave number for which bifurcation is possible. The coefficient for ion‐neutral diffusion results in a qualitatively and quantitatively meaningful diffusivity for application to the “U‐shaped” curve description of striation evolution.