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Options for Poloidal Field Diffusion Equation (PFDE) in ASTRA and TRANSP

Options for Poloidal Field Diffusion Equation (PFDE) in ASTRA and TRANSP. I. Voitsekhovitch. G. Pereverzev ISM/ITM meeting, Lisbon, 2010. Source of information: G. V. Pereverzev, P. N. Yushmanov IPP Report 5/98 2002 http://users.jet.efda.org/pages/t-task-force/Astra.pdf

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Options for Poloidal Field Diffusion Equation (PFDE) in ASTRA and TRANSP

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  1. Options for Poloidal Field Diffusion Equation (PFDE) in ASTRA and TRANSP I. Voitsekhovitch. G. Pereverzev ISM/ITM meeting, Lisbon, 2010 Source of information: G. V. Pereverzev, P. N. Yushmanov IPP Report 5/98 2002 http://users.jet.efda.org/pages/t-task-force/Astra.pdf TRANSP manual: http://users.jet.efda.org/expert/transp/Help/HelpFile/transp_help_frame.htm

  2. Motivation for this talk: D. Kalupin, ETS Code camp, July 2010, Cadarache initial q profile taken from one code may be inconsistent with total plasma current and equilibrium of another code ETS what modification of the initial q-profile should be allowed in ETS to solve this inconsistency? how this problem is solved in other codes?

  3. Options for current density evolution: • solve PFDE (ASTRA, JETTO, TRANSP) • (2) Prescribed current density evolution: • 2a: prescribed current density (ASTRA) • 2b: prescribed q (ASTRA, TRANSP) • 2c: evolve the q profile using input Bp/Bt vs (R,t) or  vs (R,t) where tan()=Bp/Bt (TRANSP) initial & bndry conditions consistency with: equilibrium? total plasma current? measured loop voltage? • TRANSP: • - time switching amongst the options (1) - (2b) and (2c) during run • in options (2b) and (2c), the solution of PFDE yields the resistivity profile (output)

  4. Poloidal field diffusion equation (PFDE)

  5. Initial condition: practically not used Measured variables are but they involve 1st or 2nd derivative of () and equilibrium (V’, G2) Two types of initial conditions: j//(,t=0) = j0() Prescribed j(r). Current density is re-normalised to be consistent with Ipl Prescribed q(r) j//() is given, E//() is calculated using resistivity model Ipl is matched by applying some adjustment procedure E//() is flat (SS), j//() is calculated using resistivity model Ipl is not matched

  6. Boundary conditions: At  =B  free-bndry code Simplified boundary conditions: a) Prescribed total plasma current: (ASTRA, TRANSP) (ASTRA, TRANSP) Total current may be not equal to experimental value b) Prescribed loop voltage: c) External circuit equation: (ASTRA)

  7. Initial q-profile and total plasma current are prescribed – adjustment procedure in ASTRA Ipl is matched by adjusting surface current density (one grid point) (3 moment equilibrium) JET 71827, JETTO run seq. 178 Current, MA q Current density, MA/m2 

  8. Initial q-profile and total plasma current are prescribed – adjustment procedure in TRANSP - user selects the adjustment region 1   1; - the entire q profile is used without modification at  < 1 - q profile is modified in the region, 1 to force consistency with total plasma current. This is done by adjusting the voltage profile using its analytic form: V() = V1 + V22 + (1 - (>1.25))2 •  is a free parameter, its value is determined by one additional constraint: •  =0 - use parabolic voltage profile • 2. match "q" at a particular radius • 3. match li/2+beta input data V1+V2 is the surface voltage, resistivity is adjusted to match total plasma current Adjusted voltage for selected resistivity model

  9. Illustration of TRANSP options for JET Hybrid Scenario 75225 • Initial q-profile in TRANSP is taken from EFIT. Total plasma current is prescribed • EFIT and TRANSP (VMEC6 = Variational Moments Equilibrium Code)equilibrium are different • Modification of q-profile at the periphery? • Effect of these modifications on q-profile evolution?

  10. Scan in initial conditions with narrow adjustment region (1=1):prescribed Ipl, q(r) and smoothed NCLASS for resistivity, calculatedV (red)prescribed Ipl, q(r) and loop voltage, calculated resistivity (blue) Resistivity,Ohm cm Current density NCLASS q zoom x10-5 Ohm cm voltage  

  11. Effect of different initial voltage on q-profile evolution q(=0) q(=0.7) Time, s

  12. Scan in the width of adjustment region (1=0.8-1):prescribed Ipl, q(r), smoothed NCLASS for resistivity and calculated voltage (red)prescribed Ipl, q(r), loop voltage and calculated resistivity (blue) 1= 1 (solid), 0.8 (dotted-dashed) 1= 1 (solid), 0.8 (dotted-dashed) Current density Current density q q voltage voltage   Modification of q is very small

  13. Strongly inconsistent initial condition – increased q with fixed plasma current. Case with prescribed Vloop and computed resistivity qref (black), 1.5*qref & 1=0.85 (red),1.5*qref & 1=0.5 (blue) q Current density Voltage 

  14. Strongly inconsistent initial condition – reduced q with fixed plasma current. Case with prescribed Vloop and computed resistivity qref (black), qref/1.5 & 1=0.85 (red),qref/1.5 & 1=0.5 (blue) q Current density Voltage 

  15. Effect of initial condition on q-evolution Case with increased q/different 1 (colour) and reference q (black) Case with reduced q/different 1 (colour) and reference q (black) q(=0) q(=0) q(=0.7) q(=0.7) Time, s Time, s

  16. Discussion: • More accurate (still simplified and fast) equilibrium model? • q adjustments and smoothing procedures? • Time switch between interpretative (prescribed q or j//) and predictive (PFDE) modes would be useful

  17. TRANSP: summary of the option with input q–profile (and dq/dt) Given the q profile, Ampere's Law can be used to get profiles of either toroidal current density Jt or the useful flux surface averaged dot product <J.B> rotB = 4j/c Then, by Faraday's law, dq/dt ==> d/d(voltage profile) and the measured surface voltage is taken as the boundary value Then the current density <J.B> and electric field <E.B> profiles are available. Driven currents are supplied from other physics models (beams, bootstrap, LH). Then, from Ohm's Law, resis*(<J.B>-<J.B>driven) = <E.B> ==> resis = <E.B>/(<J.B>-<J.B>driven) and so the results of this analysis is a resistivity profile inferred from the input data.

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