Measured Energy Transport in the MST Reversed-Field Pinch T.M. Biewer,, J.K. Anderson, B.E. Chapman, S.D. Terry 1, J.C. Reardon,, N.E. Lanier, G.Fiksel Fiksel,, D.J. Den Hartog,, S.C. Prager,, and C.B. Forest University of Wisconsin-Madison 1 University of California-Los Angeles Los Alamos National Lab M S T adison ymmetric orus Profile measurements in standard and improved confinement (Pulsed Poloidal Current Drive) plasmas have been made in the MST using recently installed or upgraded diagnostics. Estimates of electron thermal diffusivities based upon a diagonal transport relationship indicate a 5 fold reduction in core transport during. New profile information has been obtained from the following Department of Physics University diagnostics: of WisconsinT e from Thomson scattering, majority T i from Rutherford scattering, n e and n H from coupled FIR interferometry and D α arrays. Using equilibrium reconstructions, profiles are mapped onto magnetic flux coordinates, and thermodynamic fluxes (Γ, q) and forces ( n, T ) are estimated for energy and particle transport. Profile measurements are compared with theoretical models based on magnetic field stochasticity (such as those of Rechester-Rosenbluth and Harvey.) This work was supported by the U.S. D.O.E. APS DPP, UW-Madison Plasma Physics
Motivation Ongoing improvements to the diagnostic arsenal of the Madison Symmetric Torus have initiated new investigations into the plasma physics of MST transport. The use of Pulsed Poloidal Current Drive () in the past has demonstrated improved confinement in the MST, based on central electron temperature measurements and a hypothesized profile shape. Recent upgrades of the Thomson scattering system have facilitated measurements of the T e profile in the MST out to r/a=.88. These measurements, when coupled with density profiles from FIR Interferometry and MSTFIT reconstructed equilibria, have made it possible to calculate many transport quantities, including the electron thermal conductivity χ e. If the conductivity is assumed to behave as predicted by Rechester- Rosenbluth theory, then it is possible to make a direct comparison between the expected magnetic fluctuation profile and one calculated from the linear eigenfunction code, RESTER.
Outline Abstract Motivation Transport Equations Measured T e and n e Profiles MSTFIT Reconstructed Equilibrium Quantities Particle Flux and Radial Electric Field Calculations Heat Flux and Thermal Conductivity Magnetic Fluctuation Level Implications Conclusions
Transport Equations Including possible sources and sinks of energy and particles, the equations of continuity and energy balance with a radial, ambipolar electric field are: n 1 = ( rγ) + S t r p Solving for the particle and heat fluxes: 1 n e Γ 1 3 e = r rs ( pe, ) t Q= r( S + qe Γ ( nt) ) For electrons in a 3 component plasma (e -, p +, impurity Z), we can write: Spe, = nenh σiv SEe, = Pe Pei Pez Prad Pe = ηj Pei = me 4 ln( Λ) m ninee Te 3 3 Ti mete i 4ε ( ) / π P = me 4 ln( Λ) n n Z e ( T T ) / π m T ez 3 1 ( nt) = qe + t aγ ( rq) S r E 3 3 m z e 4ε e z e e Thus, an expression for E a would enable us to determine both particle and heat fluxes from measurable quantities. z r E a t Prad = Crad( r/ a) 8 Pe
Transport Equations (continued 1) The kinetically derived Fokker-Plank Equation for a plasma, including an ambipolar,, radial electric field is: v ( ) = + f par ( rdm ) qea ( rdm ) f qea f + t m r mv par v par mv par v par Taking the first two moments of this equation and comparing to the source n free continuity ( = 1 ( t r r Γ) ) and energy balance ( ( 3 nt) = qe 1 t aγ ( rq) r ) equations leads again to expressions for the particle and heat flux: ( 1 n 1 T ) Γ= Dn n + T qea T ( T qe a ) T T 1 n 3 1 Q = DnT n + By making the identification ( χ = vd t m = D), these expressions can be π combined to yield a relation for the convective and conductive parts of the heat flux: Q T n T conv cond = Γ χ Q Q r = + This process introduces two new equations, but only one additional, unknown quantity (the thermal conductivity), allowing us to solve the system and determine all the quantities of interest.
Transport Equations (continued ) measurements estimates measurements n H (r,t) n e (r,t) T e (r,t) T i T z Z eff F θ I p Γ e r rspe, n t e = 1 ( ) n i (r), n z (r), T i (r), T z (r) MSTFIT equilibrium reconstruction S E j, η, f t, B, etc. χ n n ( 1 n 1 ) T T qe T a Γ= + Q = ΓT χn T Q = 1 r( S + qe Γ ( 3nT) ) r E a t Q e,γ e, χ e, E a
Measured T e and n e Profiles T (ev) 6 5 4 3 1 Stan.-Te Ti Tz -Te Ti Tz T e (r) is measured via 6 radial points of Thomson scattering and via an insertable Langmuir probe at the edge. The combined data is fit to a cubic spline. Majority T i (~) is measured with Rutherford scattering, and the profile is estimated as T i (r)=.75*t e (r). Impurity T z is measured for C V using Ion Doppler Spectrometry, and the profile is estimated as T z (r)=.5*t e (r). n (m -3 ) 1. 1 19 1 1 19 8 1 18 6 1 18 4 1 18 1 18 Stan.-ne ni nz -ne ni nz n e (r) is measured with an 11 chord Far InfraRed Interferometer and Abel inverted using the MSTFIT code. Experimental evidence suggests Z eff ~ in the MST. With this approximation and the assumption that C V is the dominant impurity everywhere, then charge balance determines n i (r) and n z (r) from n e (r): ni + Z n n n Zjnj eni + Zenz ene = Z eff = e e z
MSTFIT Reconstructed Equilibrium 1.6 1 6 1-5 j (A/m ) 1.4 1 6 1. 1 6 1 1 6 8 1 5 6 1 5 4 1 5 resistivity (ohm m) 1-6 1 5 1-7 trapped particle fraction.6.5.4.3..1 B (T).5..15.1.5 B_t B_p B_t B_p -.5
Interchange Mode Stability Limit - - dp/dr (N/m 3 ) -4-6 -8 dp/dr (N/m 3 ) -4-6 -8-1 1 4 Suydam limit -1 1 4 Suydam limit -1. 1 4-1. 1 4 During the measured pressure gradient drops below the calculated Suydam critical pressure gradient near the edge, meaning that the plasma becomes stable to interchange modes. plasmas (and plasmas at the core) are at the limit of stability to these modes.
Particle Flux and Radial Electric Field gamma e (particles/m ) E r (V/m) 1 1 1 1 1 19 1 18 3 5 15 1 5 Stan.(gamma=) (gamma=) -5 Particle flux is calculated from an FIR interferometer (n( e ) that is co-linear with a D α array (S( p ). During there is a significant reduction in the particle source, which is manifest as a reduction in the particle flux. The core value is unresolvable with this diagnostic setup. To first approximation, the ambipolar electric field can be calculated by setting the particle flux to zero. In this case: Te ne T E a Harvey 1 e n + 1 T e, ( ) e e The deviation from the Γ e = approximation is important even at low values of flux. Γ= Dn 1 n + 1 T n T qea T
Heat Flux and Thermal Conductivity Q (W/m ) 1 1 5 8 1 4 6 1 4 4 1 4 1 4 Stan_cond Stan_conv _cond _conv Because the particle flux is largest in the edge of plasmas, it is not surprising to find that heat transport is dominated by convective losses in that region. In the region where the dominant magnetic modes of the MST are resonant conductive heat transport is very large. chi e (m /s) 1 1 1 1 Magnetic fluctuations are observed to decrease with the application of, and we see a corresponding drop in the conductive transport of heat. Electron thermal conductivity is consequently improved during, dropping by roughly a factor of 5 over the bulk of the plasma radius.
Expected Magnetic Fluctuation Level b r, calculated q (safety factor).1.1.1..15.1.5 -.5 -.1 -.15.1 -. m=1, n=6 m=1, n=7 m=1, n=8 m=1, n=1 m=1, n= m=, any n If the thermal conductivity has a Rechester-Rosenbluth Rosenbluth type from, we can calculate a profile of the expected magnetic fluctuation level: χ = D= v D t m D L b π m = eff r L = L + λ 1 1 1 eff par mfp Lpar a λ mfp >> a χ T π m abr It is experimentally observed that the magnitude of magnetic fluctuations (as measured at the edge with pick-up coils) drops during, which is consistent with this calculation, especially in the region of.15<ρ<.35 <.35 where the largest MST modes (n=6,7,8) are expected to be resonant. D m ab r
Expected Magnetic Fluctuation Level (continued).1.1 b r, calculated.1.1.1 b r (normalized RESTER).1.1.1 RESTER calculated linear eigenfunctions for b r (m=1, n=1-14) are normalized via the measured B r gradient (divb( divb= enforced pickup coils) at the edge and summed to produce the profile on the right. Though the results differ by an order of magnitude, the general trends (rising inboard of the B T reversal surface, then falling towards the core) are similar.
Conclusions Improved particle confinement in the edge of MST (transport barrier?) during results in reduced overall particle flux and reduced convective heat transport. More evidence has been presented that reinforces the notion that heat transport in the MST is driven by magnetic fluctuations. Reducing magnetic fluctuations through the application of results in the reduction of both convective but primarily conductive heat transport and a consequent increase in the overall electron temperature. The resultant pressure profile is skirting the calculated Suydam-critical limit, and suggests that residual transport in the MST during may be due to Interchange and G modes.
Reprints Full color version of this poster is available online at: http://sprott.physics.wisc.edu/biewer/apsposter.pdf