Cyclotron Heating in the MST

1. Cyclotron Heating in the MST With useful discussions with MST group Varun Tangri and P. W. Terry CMSO General Body Meeting • Durham, New Hampshire • June 2007

2. Motivation. Ion Heating In RFP machines is unexplained ! This is despite the fact that in ohmic heated plasmas, energy is predominantly dissipated as electron heat as characterized by Ohm’s Law. The unknown physical process is usually called Anomalous Ion Heating. Note: Parameters for many of these machines have improved.

3. 1 3 2 C4+ electrons During Crash: TD TC4+ Te Deuterium Motivation. Ions and impurities in MST are rapidly heated ! Before Crash: After Crash:

4. EXTRAP-T1 [Horling. PPCF (1996)] RFX [ Carraro PPCF, 2000] MST [Rostagni, PPCF (1994)] Motivation. Gas law for RFP plasmas: Temperature decreases as density increases This gives the fit [Horling. (1996)]:

5. 600 400 200 0 Other Observations. • Ion temperature increases with magnetic fluctuations • Ion heating is anisotropic EXTRAP-T2 REPUTE-1 ULQ University of Tokyo, Japan EXTRAP-T1 Stockholm, Sweden MST Horling (1996), Nagayama (1985), Z. Yoshida et. al. (1998)

6. Drive • We extend Mattor et. al. [1992] by Adding: • Losses due to confinement • Collisional exchange between electrons, bulk ions & impurities • Heating of impuirities via ICR Taylor State Free Energy A Instability Inverse cascade m=1 Cascade D To Higher wave numbers C B cascade H E G Electron dissipation F Resistivity J I K Collisional Equilibriation e-i Impurity heat losses ion heat losses e heat losses The Energy Budget (with impurities) * Anisotropic ion heating * Anisotropic collisions * Anisotropic heat losses

7. The Energy Budget (with impurities) • A previous ion heating model [Mattor et. al. (1992)] is extended to include the effect of gyro-resonant damping of cascade energy on impurity species. • The heavier mass of impurities makes them resonant at lower frequencies where more energy is present in the fluctuations. • We include Anisotropic heating, collisions and losses in the model. • Extensive simulations of this model have shown that Collisional energy transfer from anomalously heated impurities might be able to account for the observed high temperature of the bulk ions. • Finally results are compared with experimental observations cited earlier.

8. Cold Plasma terms • The species with the lowest frequency gets heated up the most. • A narrow band of frequencies close to the resonant frequency is sufficient to heat the plasma Red: EMICA of Zhang et. al Linear theory The damping of the wave can be calculated from the cold plasma dielectric tensor with warm corrections.

9. Confinement Losses Wave Heating Collisional Equilibration where Cranmer, Field and Kohl (1999) Isenberg (1984) Basic Equations.

10. Theory 90% 20% See: Bodin Nucl. Fusion 30, 1990 Results. Observations in experiments are within the range predicted by theory. Using elementary energy conservation, we can write: [ Mattor et al (1992) ] Ratio of energy forward cascaded to inverse: Fraction absorbed by fluctuations:

11. From NRL Formulary: Results. Thermal equilibration of anisotropic plasma

12. Results. • Thermal equilibration of anisotropic plasma with ICR heating Increasing density

13. 600 600 400 0 Results. • Parametric variation of heating with temperature RFP Tokamaks

14. Summary. • Previous work (Mattor et. al) is extended to include impurity species in reverse field pinch plasmas. • Impurity heating is an efficient mechanism of heating the plasma. • The heavier mass of some species allows them to be gyro-resonant at lower frequencies, where more energy is present in the fluctuations. • 'if' one impurity species could be heated to a high temperatures, it can collisionally transfer a large portion of it's energy to the bulk species, even though the density is low. • The heating of various species is dependent on density and charge state. • Heating mechanisms are highly anisotropic; however, collisions can cause the parallel temperature to attain a significant value. • fluctuations in a RFPs are orders of magnitude larger than those in a tokamak. So mechanism does not work for tokamaks.

15. Thanks