Ion Bernstein Wave Research Articles

Excitation of Large-k theta Ion-Bernstein Waves in Tokamaks.

The mode-converted ion-Bernstein wave excited in tokamaks is shown to exhibit certain very interesting behaviors, including the attainment of very small poloidal phase velocities, the reversal of poloidal direction, and up-down asymmetries in propagation and damping. Because of these effects, this wave holds promise for channeling $\ensuremath{\alpha}$-particle power to ions, something that would make a tokamak fusion reactor far more attractive than presently envisioned.

High-order ion Bernstein waves in a non-uniform magnetic field

A new approximate electrostatic dispersion relation for ion Bernstein waves with frequencies much higher than the ion gyrofrequency is considered. It is applicable for an arbitrary ion distribution function and includes resonance-broadening effects of a non-uniform magnetic field. A number of special cases are analysed.

Fast wave poloidal flow generation in a plasma

Fast wave poloidal flow generation at the plasma edge of a tokamak is studied with a one-dimensional slab model. In the absence of mode conversion, the poloidal flow can be generated by a spatial change of plasma velocity and current density profiles due to strong minority ion power absorption at the minority ion cyclotron resonance. The electromagnetic force plays a more important role in the flow generation than does the plasma Reynolds stress. In the presence of mode conversion, the flow is mainly generated by interference between the long-wavelength transmitted fast wave and the short-wavelength ion Bernstein wave (IBW) from mode conversion. Flow shear generated in the presence of mode conversion varies spatially with a scale length similar to the IBW wavelength. With mode conversion, the plasma Reynolds stress becomes more important in the flow shear generation than the electromagnetic force. For both cases, the plasma Reynolds stress and the electromagnetic force are out of phase, so that the resultant flow shear is smaller than the larger of the two. The short scale length flow shear enhances the turbulence stabilization.

Electron heating and current drive by mode converted slow waves.

An approach to obtaining efficient single-pass-mode conversion at high parallel wave number from the fast magnetosonic wave to the slow ion Bernstein wave, in a two-ion species tokamak plasma, is described. The intent is to produce localized electron heating or current drive via the mode-converted slow wave. In particular, this technique can be adapted to off-axis current drive for current profile control. Modeling for the case of deuterium-tritium plasmas in TFTR is presented.

A mechanism for beam-driven excitation of ion cyclotron harmonic waves in the Tokamak Fusion Test Reactor

A mechanism is proposed for the excitation of waves at harmonics of the injected ion cyclotron frequencies in neutral beam-heated discharges in the Tokamak Fusion Test Reactor (TFTR) [Proceedings of the 17th European Conference on Controlled Fusion and Plasma Heating (European Physical Society, Petit-Lancy, Switzerland, 1990), p. 1540]. Such waves are observed to originate from the outer midplane edge of the plasma. It is shown that ion cyclotron harmonic waves can be destabilized by a low concentration of sub-Alfvénic deuterium or tritium beam ions, provided these ions have a narrow distribution of speeds parallel to the magnetic field. Such a distribution is likely to occur in the edge plasma, close to the point of beam injection. The predicted instability gives rise to wave emission at propagation angles lying almost perpendicular to the field. In contrast to the magnetoacoustic cyclotron instability proposed as an excitation mechanism for fusion-product-driven ion cyclotron emission in the Joint European Torus (JET) [Phys. Plasmas 1, 1918 (1994)], the instability proposed here does not involve resonant fast Alfvén and ion Bernstein waves, and can be driven by sub-Alfvénic energetic ions. It is concluded that the observed emission from TFTR can be driven by beam ions.

An overview of PBX-M H-mode results

The PBX-M tokamak has an array of unique features that allow it to study regimes of enhanced confinement and stability. In particular, because of its divertor operation, PBX-M has proved to be a valuable contributor to identifying and understanding various features of H-mode physics. To be reported here are recent results of H-mode studies of m=1 bias induced H-modes, L- to H-transitions, including suppression of turbulent transport, ELMs and other related energy loss mechanisms, and Ion Bernstein Wave modification of H-mode discharges.

Theory of ion Bernstein wave induced shear suppression of turbulence

The theory of radio frequency induced ion Bernstein wave- (IBW) driven shear flow in the edge is examined, with the goal of application of shear suppression of fluctuations. This work is motivated by the observed confinement improvement on IBW heated tokamaks [Phys. Fluids B 5, 241 (1993)], and by previous low-frequency work on RF-driven shear flows [Phys. Rev. Lett. 67, 1535 (1991)]. It is found that the poloidal shear flow is driven electrostatically by both Reynolds stress and a direct ion momentum source, analogous to the concepts of helicity injection and electron momentum input in current drive, respectively. Flow drive by the former does not necessarily require momentum input to the plasma to induce a shear flow. For IBW, the direct ion momentum can be represented by direct electron momentum input, and a charge separation induced stress that imparts little momentum to the plasma. The derived Er profile due to IBW predominantly points inward, with little possibility of direction change, unlike low-frequency Alfvénic RF drive. The profile scale is set by the edge density gradient and electron dissipation. Due to the electrostatic nature of ion Bernstein waves, the poloidal flow contribution dominates in Er. Finally, the necessary edge power absorbed for shear suppression on Princeton Beta Experiment-Modified (PBX-M) [9th Topical Conference on Radio Frequency Power in Plasmas, Charleston, SC, 1991 (American Institute of Physics, New York, 1991), p. 129] is estimated to be 100 kW distributed over 5 cm.

Electromagnetic radiation by parametric decay of upper hybrid waves in ionospheric modification experiments

A nonlinear dispersion relation for the parametric decay of an electrostatic upper hybrid wave into an ordinary mode electromagnetic wave, propagating parallel to the ambient magnetic field, and an electrostatic low frequency wave, being either a lower hybrid wave or a high harmonic ion Bernstein wave, is derived. The coherent and resonant wave interaction is considered to take place in a weakly magnetized and collisionless Vlasov plasma. The instability growth rate is computed for parameter values typical of ionospheric modification experiments, in which a powerful high frequency electromagnetic pump wave is injected into the ionospheric F-region from ground-based transmitters. The electromagnetic radiation which is excited by the decaying upper hybrid wave is found to be consistent with the prominent and commonly observed downshifted maximum (DM) emission in the spectrum of stimulated electromagnetic emission.

Plasma diagnostic through ion bernstein waves

The effectiveness of a diagnostic method for both ion temperature and ion minority concentrations, based on propagation of Ion Bernstein Waves (IBW), is analysed theoretically and verified experimentally. The method is based on a comparison between wave vector measurements, obtained with an interferometric system, and theoretical dispersion relations.

A note on the toroidal plasma dispersion function

We have found a simple yet accurate approximation for the toroidal plasma dispersion function, which described the effects of parallel space dispersion on the propagation and absorption of waves near ion cyclotron resonances in tokamak plasmas. It can be easily implemented in numerical codes solving the finite Larmor radius wave equations in toroidal geometry, allowing a quantitative discussion of the effects of toroidicity on ion cyclotron damping and on linear mode conversion to ion Bernstein waves.

Excitation of electron Bernstein and ion Bernstein waves by extraordinary electromagnetic pump: Kinetic theory

In the present paper, parametric decay instability of an extraordinary electromagnetic (EM) wave into a high-frequency electron Bernstein wave and a low-frequency ion Bernstein wave is studied. The guiding center formalism is followed to obtain the coupling coefficients including kinetic effects. The momentum space integrals in the coupling coefficients are solved in the dipole approximation of the pump wave and in the limits, k⊥ρe<1 for electron Bernstein wave and k⊥ρi<1 for ion Bernstein wave. Analytical expressions for homogeneous growth rate and threshold are given explicitly. Applications of the present investigation are pointed out to ionospheric modification experiment and fusion plasmas.

Study of parametric instabilities during the ion Bernstein wave heating experiment on PBX-M

Parametric instabilities during the ion Bernstein wave (IBW) plasma heating experiment on PBX-M are investigated both theoretically and experimentally. The theoretical work shows that the RF power threshold of the instabilities is very low when the plasma density near the antenna satisfies the condition 2ωpi < ω0 << ωpe. The threshold becomes very high, >>1 MW, and is determined by convective losses due to plasma inhomogeneity when the plasma density near the antenna is sufficiently high that 0.5 < ωpi/ω0 < 1. According to the theory, the parametric instability activity should increase as the plasma is moved away from the antenna, creating a low density electron plasma wave 'gap' region. To test this hypothesis on PBX-M, the plasma position was deliberately varied while monitoring this activity. Under normal IBW operating conditions, very little parametric instability activity was observed ⩽50 dB below the pump wave (ω = ωRF). However, when the plasma edge was moved away from the antenna by about 2 cm, the parametric instability activity increased greatly, exceeding 20 dB of the pump wave. This result shows that the observed parametric instability activity can be explained in terms of the plasma inhomogeneity convective model. It was also demonstrated that, by controlling the plasma position with respect to the antenna, parametric instability activity can be controlled at a low level

Current drive by ion Bernstein waves in tokamaks

Detailed consideration is given to the problem of current drive by ion Bernstein waves (IBWs). An analytical investigation of ray tracing equations is used to prove that a significant evolution of k|| for the IBWs in tokamaks can ensure the possibility of current drive by these waves, if certain conditions are fulfilled. The main condition is the displacement of the antenna out of the midplane by a proper distance. Several scenarios for current drive are discussed, including direct excitation of the IBWs and the conversion of fast waves into IBWs. In all of these a loop antenna with a symmetrical spectrum in k|| can be used, the electron distribution function also being symmetrical in V||. The development of asymmetry in k|| for the IBWs during their propagation is caused by the gradient of the toroidal magnetic field along the major radius. Numerical calculations are also performed - for the cases of ITER and the T-10 tokamak. It is concluded that IBWs can be used as an inexpensive and effective current drive and current density profile control in tokamaks

Fast ion-driven Bernstein instabilities

A novel instability concept, namely, a two-streaming process in gyrospace, is investigated. This leads to a two-energy-stream cyclotron instability even without beams in real space, where fast ions drive electrostatic ion Bernstein waves unstable. The instability comes from the coupling of the fast and slow ion Bernstein branches due to a weak relativistic effect. When an unstable condition is satisfied, the growth rate of the cubic instability is proportional to (n f/n s) 1 3 (γ f−1) 1 3 while the efficiency ∝ (n f/n s) 1 3 (γ f−1) −2 3 . A quadratic instability dominates high harmonics at the lower-hybrid frequency regime and its growth rate has no γ f −1 dependence. The mechanism may play an important role in the interaction and dynamics of fast ions in magnetized plasmas.

Ion Bernstein wave propagation and absorption in general magnetic field configuration

A linear analysis of ion Bernstein wave (IBW) propagation and absorption is considered in a general tokamak plasma magnetic equilibrium. The effects of elongation, triangularity, and Shafranov shift on radio-frequency (rf) absorption are discussed with respect to the simple case of circular and concentric magnetic surfaces. The ray-tracing equations are analytically and numerically solved in the flux surface coordinate system, and the power deposited in the plasma is calculated along the trajectory for the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 31, 1135 (1991)] plasma parameters.

Experimental exploration of profile control in the Princeton Beta Experiment-Modified (PBX-M) tokamak

The experimental program of the Princeton Beta Experiment-Modified (PBX-M) tokamak [Phys. Fluids B2, 1271 (1990)] is directed toward tailoring plasma profiles to achieve greater stability and confinement and to gain access to the second stability region. Modification of the current density profile has been achieved with lower-hybrid current drive (LHCD), leading to a regime free of global magnetohydrodynamic modes, while raising the value of q(0) above unity. The diffusion of the fast electrons produced by LHCD has been examined using two-dimensional hard x-ray imaging. Ion Bernstein waves (IBW) have been used for ion heating: a preliminary analysis shows that ion heating was spatially localized and in agreement with theoretical calculations. Divertor biasing has modified the electric field inside the last closed surface, resulting in the formation of a transport barrier, which in turn has reduced the threshold power of neutral beam injection (NBI) for H-mode transition by 25%.

Observation of parametric decay correlated with edge heating using an ion Bernstein wave antenna on DIII-D

Significant levels of parametric decay activity and correlated edge ion heating were observed during injection of high power ion Bernstein waves (IBWs) in DIII-D. Both minority hydrogen ions and majority deuterium ions showed the formation of a high energy perpendicular tail; no parallel heating was observed. The edge ion heating and the parametric decay activity were both strongest when an ion cyclotron harmonic was present at the plasma edge. Ion tail formation had a power threshold of several hundred kilowatts, above which the tail size increased with antenna power; a comparable power threshold for parametric decay instability (PDI) was observed. Both the PDI and the associated edge deuterium heating were found to be sensitive to the hydrogen-to-deuterium ratio

Ion Bernstein wave antenna loading measurements on the DIII-D tokamak

Antenna loading measurements carried out during high power ion Bernstein wave (IBW) heating experiments on the DIII-D tokamak indicate that efficient, direct coupling to the IBW at ω ≲ 2ωci as predicted by linear coupling theory did not occur. Whereas strong peaking in the loading resistance near cyclotron harmonics is predicted for high edge densities (ω < ωLH|edge), the observed loading resistance is nearly independent of the toroidal magnetic field. The loading anomaly can be explained by invoking the ponderomotive force which decreases the edge density immediately in front of the antenna, thus allowing coupling to the cold plasma lower hybrid wave (LHW). A linear LHW coupling code including the modified density profile due to the ponderomotive force reproduces the measured dependence of antenna loading on toroidal magnetic field, edge density, antenna frequency and antenna phasing. Further evidence for the ponderomotive force is obtained from reactive loading measurements which indicate that the plasma is pushed away from the antenna as the radiofrequency power level is increased. The results indicate that the lack of central ion heating observed during DIII-D IBW experiments may be due to a lack of efficient mode transformation from the coupled LHW to a centrally propagating IBW, possibly as a result of nonlinear mechanism(s)

Nonlinear ion Bernstein wave heating experiment in the WT-3 tokamak

Ion Bernstein wave (IBW) heating at ion cyclotron half-harmonic frequencies was performed in hydrogen (H) discharges in the WT-3 tokamak. The bulk ion temperature increase was measured by a charge exchange analyser and a spatially scanning polychrometer. The latter diagnostics can provide radial ion-temperature profiles. The incremental ion temperature has shown a peak at the exact location where the IBW frequency omega equals 3/2 of the ion cyclotron frequency, indicating the nonlinear direct acceleration of H ions. The wave electric field was measured by a Langmuir probe in the scrape-off layer. The electric field at the second harmonic of the excited IBW frequency was observed to vary depending on the power level and the toroidal magnetic field. These experimental results are compared with the theoretical prediction of nonlinear IBW damping. The measured dependences of the ion heating and the wave amplitude at 2 omega on the toroidal magnetic field are in reasonable agreement with the prediction.

Ion Bernstein wave heating research

Ion Bernstein wave heating (IBWH) utilizes the ion Bernstein wave (IBW), a hot plasma wave, to carry the radio frequency (rf) power to heat the tokamak reactor core. Earlier wave accessibility studies have shown that this finite-Larmor-radius (FLR) mode should penetrate into a hot dense reactor plasma core without significant attenuation. Moreover, the IBW’s low perpendicular phase velocity (ω/k⊥≊VTi≪Vα) greatly reduces the otherwise serious wave absorption by the 3.5 MeV fusion α particles. In addition, the property of IBW’s that k⊥ρi≊1 makes localized bulk ion heating possible at the ion cyclotron harmonic layers. Such bulk ion heating can prove useful in optimizing fusion reactivity. In another vein, with proper selection of parameters, IBW’s can be made subject to strong localized electron Landau damping near the major ion cyclotron harmonic resonance layers. This property can be useful, for example, for rf current drive in the reactor plasma core. IBW’s can be excited with loop antennas or with a lower-hybrid-like waveguide launcher at the plasma edge, the latter structure being one that is especially compatible with reactor application. In either case, the mode at the plasma edge is an electron plasma wave (EPW). Deeper in the plasma, the EPW is mode transformed into an IBW. Such launching and mode transformation of IBW’s were first demonstrated in experiments in the Advanced Concepts Torus-1 (ACT-1) [Phys. Rev. Lett. 45, 1105 (1980)] plasma torus and in particle simulation calculations. These and other aspects of IBW heating physics have been investigated through a number of experiments performed on ACT-1, the Japanese Institute of Plasma Physics Tokamak II-Upgrade (JIPPTII-U) [Phys. Rev. Lett. 54, 2339 (1985)], the Tokyo University Non-Circular Tokamak (TNT) [Nucl. Fusion 26, 1097 (1986)], the Princeton Large Tokamak (PLT) [Phys. Rev. Lett. 60, 294 (1988)], and Alcator-C [Phys. Rev. Lett. 60, 298 (1988)]. In these experiments both linear and nonlinear heating processes have been observed. Interestingly, improvement of plasma confinement was also observed in the PLT and Alcator-C experiments, opening up the possible use of IBW’s for the active control of plasma transport. Two theoretical explanations have been proposed: one based on four-wave mixing of IBW with low-frequency turbulence, the other on the nonlinear generation of a velocity-shear layer. Both models are consistent with the observed threshold power level of a few hundred kW in the experiments. Experiments on lower field plasmas on JFTII-M [Eighth Topical Conference on Radio-Frequency Power in Plasmas, Irvine, CA, 1989 (American Institute of Physics, New York, 1989), p. 350] and DIII-D [Eighth Topical Conference on Radio-Frequency Power in Plasmas, Irvine, CA, 1989 (American Institute of Physics, New York, 1989), p. 314] have raised some concern with the IBW wave-launching process. The experiments showed serious impurity release from the walls but little or no core heating, a combination of circumstances strongly suggestive of edge heating. Possible parasitic channels could include the excitation of short wavelength modes by the Faraday shield’s fringing fields, antenna-sheath-wave excitation, an axial-convective loss channel, and nonlinear processes such as parametric instability and ponderomotive effects. Suggested remedies include changes in the antenna phasing, the use of low-Z insulators, operating at higher frequencies, positioning the plasma differently with respect to the antenna, eliminating the Faraday shields, and using a waveguide launcher. The recent JIPPTII-U experiment, employing a 0-π phased antenna array with a higher frequency 130 MHz source, demonstrated that those remedies can indeed work. Looking to the future, one seeks additional ways in which IBWH can improve tokamak performance. The strong ponderomotive potential of the IBWH antenna may be used to stabilize external kinks and, acting as an rf limiter, to control the plasma edge. Control of the plasma pressure profile with local IBWH heating is already an important part of the Princeton Beta Experiment-Modified (PBX-M) [Ninth Topical Conference on Radio-Frequency Power in Plasmas, Charleston, SC, 1991 (American Institute of Physics, New York, 1991), p. 129] program in its exploration of the second-stability regime. Application of IBWH may also improve the performance of neutral beam heating and the efficiency and localization of lower-hybrid current drive for current profile control. Used with pellet injection, IBWH may also prolong the period of good confinement. The three planned high-power IBWH experiments covering vastly different parameters: f=40–80 MHz for PBX-M; f=130 MHz for JIPPT-II-U; and f=430 MHz for the Frascati Tokamak-Upgrade (FT-U) [16th European Physical Society Conference on Controlled Fusion and Plasma Physics, Venice, Italy, 1989 (European Physical Society, Amsterdam, 1989), Vol. III, p. 1069] appear to be well positioned to explore these possibilities and to clarify other issues including the physics of wave launching and associated nonlinear processes.