Lower Hybrid Wave Induced Rotation on Alcator C-Mod* Ron Parker, Yuri Podpaly, John Rice, Andréa Schmidt *Work supported by USDoE awards DE-FC-99ER551 and DE-AC-7CH373
Abstract Injection of RF power in the vicinity of the lower hybrid frequency has been observed to cause strong counter current rotation in Alcator C-Mod plasmas[1,]. The spin-up rate is consistent with the rate at which momentum is injected by the LH waves, and also the rate at which fast electron momentum is transferred to the ions. A momentum diffusivity of ~.1 m^/s is sufficient to account for the observed steady-state rotation. This value is also comparable with that derived from an analysis of rotation induced by RF mode conversion. Radial force balance requires a radial electric field, suggesting a buildup of negative charge in the plasma core. This may be the result of an inward pinch of the LH produced fast electrons, as would be expected for resonant trapped particles. Analysis of the fastelectron-produced bremsstrahlung during LH power modulation experiments yields an inward pinch velocity of ~ 1 m/s, consistent with the estimated trapped particle pinch velocity. [1.] A. Ince-Cushman, et.al., Phys. Rev. Lett., 1, 35 (9) [.] J. E. Rice, et. al., Nucl. Fusion 9, 5 (9)
Examples of discharges with substantial LH-induced counter rotation MA 18317. I p.5 V Vl n = 1.9 n = 1. MA 18313. I p.5 V Vl MW 1 19 /m 3 3 1. 1 8 <n e > T e () LH T rad.5 1.5. t (s) MW 1 19 /m 3 3 1. 1 8 <n e > T e () LH T rad.5 1.5. t (s) Discharge in right panel has stronger current drive, current profile modification. MHD activity occurs at t = s in this discharge, affecting profile evolution
These discharges have q()>1 and are sawtooth stabilized Ohmic Behavior of central q and internal Inductance (from EFIT) are consistent with broadening of j φ profile. n ll =1.95 Time(s) l i J φ (MA/m ) 1 n ll =1.5 R(m) Time(s) For EFIT reconstruction P and FF are modeled by - and 3- term polynomials, respectively, and poloidal field on mid-plane is constrained by MSE measurements. Any structure in j φ (R) is smoothed by this approach.
.. 8 1. 1. 1... 8 1. 1. 1... 8 1. 1. 1. km/s Spatial profiles show LH-driven counter rotation is localized to core V - Tor - - 18317 n = 1.9 18317 V.5 V l Time MW. 1 8 LH T rad. 1. 1. t (s) Rotation overshoots at beginning and end of LH pulse V tor (km/s) Time (t =.9) 18317 Central rotation increases after turnoff Of LH power See also shot 18313 (t = 1.199)
.. 8 1. 1. 1... 8 1. 1. 1... 8 1. 1. 1. km/s V Rotation increases with lower n ll, but MHD activity develops and clamps rotation - - -.5 18313 V Tor V l n = 1. Time 18313 MW. 1 8 LH T rad. 1. 1. t (s) Lower n ll is more effective at current profile modification, drives central q > 1 Time ( t =.9) (t=.935)
Instability is a virulent m=, n=1 mode q = location (?) (t=.935) Rotation rapidly slows as instability grows Assuming mode frequency tracks rotation velocity, i.e., ω ~ k V tor at resonant position, location can be identified corresponding to q= r r
MSE signals show response to LH current drive, MHD = 1. instability for n MA MW 18313. I p.5 V Vl 1 19 /m 3 3 1. 1 8 <n e > T e () LH T rad.5 1.5. t (s) Arctan(B v /B φ ) (degrees) Time(s) MSE traces at various major radii for shots with MHD. Onset of MHD activity modifies MSE profile.
After LH, rotation transiently redevelops, then decays.. 8 1. 1. 1... 8 1. 1. 1... 8 1. 1. 1. 18313 18313 km/s - - V Tor V MW -.5. 1 8 LH V l T rad. 1. 1. t (s) V tor (km/s) Time Time (t= 1.11) Recovery after LH pulse suggests a role for internal electric field and/or fast Electrons. (t= 1.5)
Rate of injected wave and particle momentum is sufficient to explain plasma momentum buildup Rate of toroidal momentum buildup in plasma: P& ϕ = minv& ϕ Vol =.x1 3 N Rate of momentum injected by wave 1 : P& ϕ r 1 r = da sk r ˆ ϕ = ω =. 7x1 3 N n ϕ c da W r v g ˆ ϕ = n ϕ c Power Rate at which fast current carrying electrons lose momentum: P& ϕ = πr dam ( nv) fast πrmei = = 5.7x1 τ eτ e 3 SD 1 A. Bers in Plasma Physics Les Houches 197, G. DeWitt and J. Peyraud, eds, Gordon and Breach(1975) SD N
Wave momentum transferred to trapped electrons also results in inward pinch d dt Δψ δr v r ( mr 1 en B t & φ eψ ) ψ = r p dp dt ϕ = ere RE ϕ ϕ dt TR e dp dt ϕ v r.7 Numerically, m/s (inward) Buildup of negative charge in core would result in a radial electric field, which through radial force balance requires toroidal rotation
A hard x-ray camera measures fast electron bremsstrahlung resolved in time, space & energy C-Mod Cross Section J. Liptac, RSI, 77, 135 () HXR Diagnostic a c =5 mm a d =5 mm 3 chords ~ 1 cm spatial resolution ~ 1 µs time resolution D=13 cm d= cm Post-processing of raw pulse train for pulse height analysis and time/energy binning
Analysis of modulated bremsstrahlung emission yields evidence for inward pinch of fast electrons LH pulse is square-wave modulated and Bremsstrahlung is sorted into time and and energy bins emissivity (counts/(mm 3 str s)) 7 5 3 1 PLH (t) x 1 5 ms Scan across plasma vertical cross-section t Inversion Example. 1 sqrt(ψ t ) ~ r/a Model for fast electron density, n(r,t,e): n n = + ( D n) ( nv) + S t τ By comparing buildup and decay with this diffusion-pinch model, a pinch velocity can be backed out: - - - - - 1 1. 1. 1. v (m/s) 1.8 5 7 8 HXR Energy ()
1.1 1. 1.3 1. 1.5 1.1 1. 1.3 1. 1.5 In low density H-modes, LH Waves modify pedestal.... 1 P ICRF (MW) W MHD (kj) 5 3.75.5 3 Te, () 1. Te, r/a~5.5. 1.5 1.5.5 V surf (V) n e (1 m -3 ) P rad (MW) P LH (MW) 1.1 1. 1.3 1. 1.5 time (s) Pedestal density decreases, profile broadens Pedestal temperature increases, leading to increased temperature and stored energy (a) (b) (c) (d) (e) (f) (g) n e (1 m -3 ) T e () p e (kpa) Edge pedestal: LH off / LH on LH ON LH ON R - R LCFS (mm) Jerry Hughes, B13.
.. 1.. 1.... and edge rotation, which propagates to core. P LH ΔVφ (km/s) ΔVφ (km/s) - - - Line-integrated density Pedestal & near SOL density Pedestal toroidal rotation change (B + ) Central toroidal rotation change (Ar +1 ) Pedestal rotation change occurs before change in core rotation LH also increases SOL density, decreases density in pedestal and core SOL density profile broadens These H-modes will be a focus for LHCD studies in the next campaign
The LH induced rotation appears to be additive to ICRF induced rotation
Summary Injection of Lower Hybrid Waves into Alcator C-Mod plasmas generates strong counter rotation in core Injected wave momentum is sufficient to account for momentum buildup, but mechanism for generation of momentum is unclear, in particular role of radial electric field Analysis of hard X-Ray bremsstrahlung suggests a pinch mechanism for fast electrons, supporting development of negative radial electric field and counter-rotation In higher density H-Modes Lower Hybrid Waves affect edge, resulting in pedestal density relaxation and edge counter rotation which reduces ICRF induced co-rotation in core.