Fast-Electron-Driven Instability in the HSX Stellarator C. Deng and - PowerPoint PPT Presentation

Fast-Electron-Driven Instability in the HSX Stellarator C. Deng and D.L. Brower University of California, Los Angeles D.A. Spong Oak Ridge National Laboratory B.N. Breizman University of Texas, Austin A.F. Almagri, D.T. Anderson, F.S.B. Anderson, W. Guttenfelder, K. Likin, J. Lore, J. Lu, J. Schmitt, K. Zhai University of Wisconsin-Madison

Outline 1. Characteristics of observed fluctuation - frequency - mode number - scaling 2. Candidates of Instability - Alfvenic - acoustic - other?

HSX major radius: 1.2 m minor radius: 0.15 m magnetic field: 0.5 T 28 GHz ECRH: <150 kW pulse length: < 50 ms

Flux Surfaces and Interferometer Chords Interferometer System: 1. 9 chords 2. 200 kHz B.W. 3. 1.5 cm chord spacing

Coherent Density Fluctuations during QHS QHS plasma Heating: - 28 GHz ECRH - 2nd Harmonic X-mode for B T =0.5T generates fast T e   T e // electrons T e  700 eV - Bulk T i  20 eV ฀ ฀ For P ECRH > 100 kW, mode degrades confinement, - perturbs particle orbits leading to enhanced loss

Fluctuation Features • Only observed in QHS plasmas density measurement • m=odd, >1?, n=1 (density) • m=?, n=1 (magnetic) • Satellite appears at low densities, D f~20 kHz • Propagates electron drift direction • magnetic and density perturbation m=odd (>1) higher f peaks at larger r/a

Fluctuation Mode not Observed in 1 Tesla QHS Plasma Magnetic Field Fluctuations Density Fluctuations Fundamental O-mode ECRH for B T =1T does not drive energetic electron population => no drive for fast-electron mode

Quasi-Helically Symmetric (QHS) configuration Normal mode Alfvén continua: n = 1 mode family • B=0.5 T 0 - 50 kHz for m=1,n=1 n e (0)=1.8x10 12 cm -3 (1,1)=(m,n) • Only minor changes for mirror configuration • Observed mode frequency is near Alfven continuum for (1,1) • Continuum frequency errors at 20% due to iota sensitivity E r effects on  unknown • f measured   V       A m n Alfven R   2   GAM 1 2    A 2 STELLGAP code (D. Spong) including ad hoc pressure term: ฀

Mode Frequency Scaling with Electron Temperature 1            2 2 2   V 2 T 7 T Breizman, PoP 12 ,112506(2005) 1 2              2 2 2   A e i m n 1 1     A GAM 2 2      R m R 4 T 2  i e - vary P ECRH and hold n e constant 1          2 2 2 T 7 T           e i 1 1     GAM 2      m R 4 T 2  i e   V       A m n Alfven R o: f mode measured o: f mode measured n e = 3x10 12 cm -3 B T = 0.5 T T i = 20 eV T e scaling consistent with finite pressure effects even at low 

Mode Frequency Scaling with iota (  =1/q)   1 2      2 2 A GAM 1          2 2 2   V 2 T 7 T         2   A e i m n 1 1     2 2      R m R 4 T 2  i e   V       A (1,1) m n Alfven R o : f mode measured for fixed density and temperature…. no frequency scaling for (  < 1.04) is consistent with finite pressure effects 1. no frequency scaling for (1.04 <  <1.10) suggests mode is not Alfvenic… 2. ……..acoustic mode insensitive to iota

Frequency scaling with ion mass density Hydrogen B Deuterium V Alfven    1 2 Helium Mn ---- V Alfven 1 2   C s  T e     M   k // C acoustic s ฀ Mode frequency scaling with density ……. 1. Mass scaling for Alfvenic and acoustic modes is identical 2. Temperature also scales with density - If T e ~1/n e , V Alfven and C s would be indistinguishable from density scaling - B scaling not possible due to ECRH heating

HSX Provides Access to Configurations With and Without Symmetry QHS: helical axis of symmetry in |B| Mirror: quasi-helical symmetry broken by adding a mirror field. QHS Mirror Red  |B|  0.5 T Blue  |B|<0.5 T QHS:Helical Bands of Mirror: Helical Bands Constant |B| are Broken

Coupled Equations for Acoustic and Shear Alfven Waves Lagrangian Formulation  2  g 4  ( B  ) g 1      G  t 2  B 2 ( B  )   C s B  2    G  B 2 B 2  2       C s    t 2  C s 2 ( B  ) B  2 ( B  )  G   Notations: C s (  )  sound speed G     curl B is a coordinate-dependent coupling   B 2   factor (related to curvature ) B  equilibrium magnetic field   equilibrium mass density ฀   g      is a component of metric tensor   shear Alfven eigenfunction   acoustic eigenfunction ฀ Equations capture Alfven continuum, acoustic continuum and GAM

Coupled Alfvenic-Acoustic Modes (m,n) (3,3) (4,4) B V Alfven    1 2 Mn (2,2) (1,1) 1 2   C s  T e     M ฀ (7,1) f measured (5,1) (3,1)

Coupled Alfvenic-Acoustic Modes f=34 kHz acoustic: m=3, n=1 Alfvenic: m=1, n=1   k // A V Alfven  k // s C s r/a=0.267 A  k // V Alfven  C s  k // s - Mode is largely acoustic……. - Alfvenic and acoustic modes have different m,n Continuum code: D. Spong ฀

Coupled Alfvenic-Acoustic Modes f=67 kHz acoustic: m=5, n=1 Alfvenic: m=1, n=1   k // A V Alfven  k // s C s r/a=0.267 A  k // V Alfven  C s  k // s - Mode is largely acoustic……. - Alfvenic and acoustic modes have different m,n ฀

Coupled Alfvenic-Acoustic Modes f=100 kHz acoustic: m=7, n=1 Alfvenic: m=1, n=1   k // A V Alfven  k // s C s r/a=0.267 A  k // V Alfven  C s  k // s - Mode is largely acoustic……. - Alfvenic and acoustic modes have different m,n ฀

Coupled Alfvenic-Acoustic Modes (m,n) (3,3) (4,4) B V Alfven    1 2 Mn (2,2) (1,1) 1 2   C s  T e     M f lab  f mod e  f Doppler ฀  f mod e  1 2  k  v Doppler (7,1)  f mod e  m E r (5,1) 2  B o r (3,1) 5  10 kHz ;  E r  5 V / cm ฀

Mode Structure f=53 kHz (1,1) r/a=0.2 magnetic  density (0,3) 

Mode not observed when Quasi-Symmetry Broken Scaling with Mirror perturbation Acoustic mode V //  C s (magnetic ripple) V // m V   V th  V  M D B B  V // m  M  0.025 V  Alfvenic mode V //  V A V   V th ฀ D B B  V // m 1   0.25  V  M (conventional stellarator configuration: ~10% mirror perturbation) ฀ Acoustic mode much more sensitive to magnetic ripple

Mode not observed when Quasi-Symmetry Broken V // resonance lost when …. D B Acoustic mode 1 D B 2 2 mv  D v //  v  B  C s    cons tan t magneticmoment : B D B B  m E Tot  1    cons tan t 2  v  2 Totalenergy : 2 m v // M E Tot  1 m 2   B  2 D ( v // 2 )   D B  0 2 mv // ฀ ( D v // ) 2  2  2 D B Alfvenic mode m D B  v  B D B D v //  v  B  V A Magnetic Ripple D B B  m 1 12   D v //  D B ฀ v   v th    M   v  B Acoustic mode much more sensitive to magnetic ripple ฀ ฀

Fast Electron Driven Instability in HSX Mode identification … If Alfvénic instability: with finite pressure effects - continuum calculation shows m=n=1 is only candidate - for low m,n: mode frequency is very sensitive to iota (new) data show 1) m>1(?) 2) mode frequency not sensitive to iota 3) mode sensitive to magnetic ripple 3)  =k // V A varies strongly with radius leading to phase mixing Other mode candidates…. Acoustic instability (coupled to shear Alfven wave) - m>1 expected - no iota scaling sensitivity -  =k // C s fairly constant with radius e >>T i ….small Landau damping - T - very sensitive to mirror term Drift modes under consideration……

Future Plans….. • Theory: - continue to investigate what mode it could be, calculated the mode growth (damping) rates and their relationships with magnetic ripple - calculate the eigenmode radial structure Experimental: - determine magnetic mode number (m,n) using newly installed magnetic probe arrays - Compare interferometer and magnetic coil data with theory calculation.

Some thought for the slide 20 2. Ratio of C s /V A 1. Resonant conditions   V For Alvenic 1       A  m n C S V Alfven R A      For acoustic k // C acoustic s 3. Formulas in Slide 23 v  v why ?  th I am not sure I could explain clearly why the acoustic mode is much more sensitive to magnetic ripple.