A sharp transport barrier, accompanied by a bifurcated poloidal rotation and a radial electric field, is formed at the plasma edge by driving a radial current across the outer magnetic surfaces of a tokamak. A decrease in particle transport is observed for negative radial E fields. When the radial current is turned off, the E field and the rotation damp on a time scale comparable with the ion-ion collision time.PACS numbers: 52.25.Fi, 52.55.Pi, 52.70.Ds An intensive effort is in progress, worldwide, to correlate the large and growing data base of experimental observations on plasma transport in magnetic fusion containment devices with theoretical models. In particular, the so-called "//^-mode" regimes in tokamaks have attracted strong interest due to their enhanced particle and energy confinement properties. ^""^ The transition of a plasma into the H mode is marked by a sudden decrease in the hydrogenic light emission from the plasma edge, followed by a prolonged increase in the plasma density. The reduction of hydrogen light (H^ or H^) indicates that the incoming neutral particle flux is reduced, presumably because of a decrease of the outgoing plasma flux, leading to a reduction in "recycling." The improvement in the energy confinement is generally less than the increase in particle confinement, ^-mode measurements also reveal the formation of sharp density and temperature gradients inside the last closed magnetic surfaces, which represents a transport barrier. Despite the magnitude of the effort aimed at modeling the H mode, no clear mechanism has been identified, although radial electric fields are thought to play a role."*'^ In this Letter, experimental observations confirming the importance of the radial E field and the associated plasma rotation for 7/-mode confinement are presented.In 1979, electron injection was used to modify the edge potentials in order to reduce ion sputtering in the Macrotor tokamak.^ Subsequently, improved particle confinement and a concomitant impurity accumulation were observed,^ apparently giving rise to an H mode. These effects were attributed to the creation of edge radial electric fields and associated negative plasma potentials much larger in magnitude than Tgia), where a is the plasma radius. Recently we have extended this earlier work using the new, titanium-gettered. Continuous Current Tokamak (CCT) at the University of California, Los Angeles. The recent experiments clearly show the //-mode signatures found in other tokamaks in various limiter, divertor, and auxiliary-heating configurations. The previously seen impurity limitations^ have also been eased by new electrode designs. ^ For the //-mode-regime studies, CCT was operated in the pulsed neo-Alcator regime, with central parameters R^l.5 m, a =0,4 m, Bt=3 kG, /p=50 kA, ne=5 xlO*Vcm^ Kioop<1.5 V, Te>l50 eV, and T/> 100 e = 180 INSULATOR ELECTRODE = 0" C/2 Q 1.5 1.8 MAJOR RADIUS (M) FIG. 1. (a) Cross section of tokamak, a ^40 cm, showing the location of the exciting electrode, re ^25 cm, and the "rake" probe arrays used...

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Linearized, longitudinal waves in a hot plasma include, besides the familiar electron plasma oscillations, in which the frequency ω is of order ωp = (4πne2/m)½, also ion plasma oscillations with ω ≈ ωp(m/M)½. The properties of the latter are explored using a Vlasov equation description of the plasma. For equal ion and electron temperatures, Te = Ti, there exists a discrete sequence of ion oscillations, but all are strongly damped, i.e., have -Im ω/Re ω ⪞ 0.5, and hence are not likely to be observable. The ratio Im ω/Re ω can be made to approach zero (facilitating detection of the waves) by either increasing Te/Ti or by producing a current flow in the plasma. In the latter case, Im ω can even be made positive (corresponding to growing waves), the current required for this being smaller the larger the value of Te/Ti. This growing wave is just the familiar two-stream instability which is thus seen to be an unstable ion oscillation. It is also noteworthy that the ion oscillations, which for small k have the properties usually associated with an acoustic wave (longitudinal polarization, ω ∝ k), are obtained using a formalism which is sometimes designated as ``collisionless.''

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The transformation of electromagnetic waves into Langmuir oscillations (and vice versa) is explicitly examined in the vicinity where the wave frequency matches the electron plasma frequency in an inhomogeneous plasma. For an unmagnetized plasma with a linear density profile of scale length L, closed-form, analytic expressions are derived, in terms of Airy functions, for the reflection and mode conversion coefficients of Langmuir and electromagnetic waves utilizing a source approximation that is valid when the electromagnetic field scale length is large compared to that of the electrostatic field. The technique developed to determine the energy flux coefficients and the fields is general enough to apply to a plasma with a profile other than a linear one, and should prove useful in other problems where a scale length separation is valid. The reflection coefficient for the ‘‘direct’’ problem (incident electromagnetic wave) is equal in magnitude to that of the ‘‘inverse’’ problem (incident electrostatic wave) and the corresponding mode conversion coefficients satisfy energy conservation. The mode conversion coefficient of the warm, collisionless problem is independent of electron temperature, T, in the limit of small T, and is equal in magnitude to the mode conversion coefficient of the cold, collisional problem, which is likewise independent of the collision frequency. It also depends on the angle of incidence θ and the vacuum scale length k0L, and for T/mc2≪1, agrees with earlier, numerical calculations.

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The two-stream instability is examined for the case of an ion beam traversing a plasma. The dispersion equation for linearized, longitudinal waves in a plasma where collisions are negligible is used to find the restrictions on beam velocity, temperature, and density which will lead to growing waves.

The sheath formed between a magnetized plasma and a particle absorbing wall is examined for the case in which the magnetic field intercepts the wall at a small angle 0°&lt;ε≲9°, where sin ε=B⋅n̂/‖B‖, and n̂ is the unit normal to the wall. The model is time-independent and one-dimensional (1-D) with all functions varying only in the direction normal to the wall. The ions are modeled by a Maxwellian velocity distribution which is modified by the condition that ions, which would have hit the wall, are absent. For the electrons a fluid description is used, including the effects of electron–neutral collisions. The transport of particles due to turbulent electrostatic fluctuations is modeled by a constant electric field perpendicular to both B and n̂. It is found that in the range of angles under consideration, there are two distinct regimes of sheath formation. If ε≲ν̄=ν/Ωe (grazing incidence), where ν is the electron–neutral collision frequency and Ωe is the electron cyclotron frequency, then the properties of the sheath are determined by a parameter λ which is the ratio of the convective (E×B) and diffusive electron flows. If λ≲1, the wall potential is negative and the sheath scale length is on the order of an ion gyroradius. If λ≳1, the wall potential is positive and, for large λ, the sheath is characterized by two scales: a short length, which is a decreasing function of λ, adjacent to the wall, and the ion gyroradius farther from the wall. For ε≫ν̄, (oblique incidence) the potential at the wall is negative with a magnitude close to that of the unmagnetized plasma and is only weakly dependent on ε. In addition, for this case, the sheath scale length is on the order of an ion gyroradius and is weakly dependent on ε, larger values of ε resulting in a slightly shorter scale length.