normal mode approach to modeling of feedback stabilization of the resistive wall mode n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
NORMAL MODE APPROACH TO MODELING OF FEEDBACK STABILIZATION OF THE RESISTIVE WALL MODE PowerPoint Presentation
Download Presentation
NORMAL MODE APPROACH TO MODELING OF FEEDBACK STABILIZATION OF THE RESISTIVE WALL MODE

Loading in 2 Seconds...

play fullscreen
1 / 17

NORMAL MODE APPROACH TO MODELING OF FEEDBACK STABILIZATION OF THE RESISTIVE WALL MODE - PowerPoint PPT Presentation


  • 141 Views
  • Uploaded on

NORMAL MODE APPROACH TO MODELING OF FEEDBACK STABILIZATION OF THE RESISTIVE WALL MODE. By M.S. Chu(GA), M.S. Chance(PPPL), A. Glasser(LANL), and M. Okabayashi(PPPL). Acknowledgement to A. Bondeson, Y.Q.Liu. Nucl. Fusion Vol. 43 , 441 (2003). MOTIVATION.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'NORMAL MODE APPROACH TO MODELING OF FEEDBACK STABILIZATION OF THE RESISTIVE WALL MODE' - quiana


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
normal mode approach to modeling of feedback stabilization of the resistive wall mode

NORMAL MODE APPROACH TO MODELING OF FEEDBACK STABILIZATION OF THE RESISTIVE WALL MODE

By

M.S. Chu(GA), M.S. Chance(PPPL),

A. Glasser(LANL), and M. Okabayashi(PPPL)

Acknowledgement to

A. Bondeson, Y.Q.Liu

Nucl. Fusion Vol. 43, 441 (2003)

Feedback Workshop, Austin

motivation
MOTIVATION
  • To develop a model for understanding results from experiments (DIII-D) on feedback stabilization and to evaluate performance of future devices (ITER)
  • To develop a model beyond the usual model which includes only the geometrical effects from the slab or cylindrical geometry, i.e. Grad-Shafranov equilibrium
  • To compare and benchmark with results from other codes

Feedback Workshop, Austin

normal mode approach nma based on energy conservation of general plasma equilibrium
NORMAL MODE APPROACH (NMA) BASED ON ENERGY CONSERVATION OF GENERAL PLASMA EQUILIBRIUM
  • Perturbation energy of RWM for ideal plasma
    • General plasma equilibrium: axi-symmetric or helical
    • General plasma perturbation: axisymmetric or helical
    • Frequency dependent non-self-adjoint

DW

Kinetic Energy

Coil Excitation Energy

Wall Dissipation

Plasma

WP, K

EC

Vacuum

WV

Feedback Workshop, Austin

nma based on the normal modes of the open loop operation
NMA BASED ON THE NORMAL MODES OF THE OPEN LOOP OPERATION
  • NMA applicable if open loop system can be represented as a set of normal modes
    • No plasma rotation
    • No plasma dissipation
    • A more conservative model than MARS-F
  • The details of the system is completely described
    • Does not rely on Pade approximation

Feedback Workshop, Austin

three steps for full solution
THREE STEPS FOR FULL SOLUTION
  • Open loop stability: Generalization of the ideal MHD stability problem (no feedback)
  • Evaluate the excitation and sensor matrices of the feedback geometry
  • Evaluate feasibility of feedback based on Nyquist diagram or characteristics equations

DW

Plasma

WP

EC=0

Vacuum

WV

Feedback Workshop, Austin

nma implemented by coupling dcon vacuum tank
NMA IMPLEMENTED BY COUPLING DCON + VACUUM + TANK
  • DCON expresses plasma free energy in terms of perturbed magnetic field at plasma boundary
  • Extended VACUUM expresses vacuum energy in terms of perturbed magnetic field at plasma boundary and the vacuum tank
  • Tank evaluates the energy dissipation in terms of the perturbed

Feedback Workshop, Austin

currents on vacuum vessel represented as a set of dissipation eigenfuctions
CURRENTS ON VACUUM VESSEL REPRESENTED AS A SET OF DISSIPATION EIGENFUCTIONS
  • Flux leaking through the resistive wall excites dissipation eigenfunctions

Odd

Induced by

toroidal

efffect

even

Poloidal position along the resistive wall

Feedback Workshop, Austin

grad shafranov solver toq and dcon analysis determines rwm stability boundaries
GRAD-SHAFRANOV SOLVER (TOQ) AND DCON ANALYSIS DETERMINES RWM STABILITY BOUNDARIES

Equilibrium Flux Function

Pressure

W from

Dcon

Safety factor

Plasma

Vacuum

Total W

Feedback Workshop, Austin

eddy cuurents of open loop stability eigenfunctions
EDDY CUURENTS OF OPEN LOOP STABILITY EIGENFUNCTIONS

2nd Stable Mode

  • Computed also by MARS

Unstable RWM

Poloidal angle

Toroidal angle

3rd Stable Mode

1st StableMode

Feedback Workshop, Austin

characteristics equation of closed loop system determines rwm feedback
CHARACTERISTICS EQUATION OF CLOSED LOOP SYSTEM DETERMINES RWM FEEDBACK
  • Closed loop feedback stability described by a compact set of equations for open loop amplitudes iplus coil currents IC
  • Diagonalization of the open loop response allow reduction of the dynamical variables to (I, Ic)

Characteristics Equation

Response to Feedback Coils

Open Loop Eigenfunction

Excitation Matrix

Identity Matrix

Sensor Matrix

Gain Matrix

Feedback Workshop, Austin

single input and single ouput can be analyzed using nyquist diagram
SINGLE INPUT AND SINGLEOUPUT CAN BE ANALYZED USING NYQUIST DIAGRAM

0 = No Wall 1 = Ideal wall

  • Stablized if transfer function P() encircles (-1,0)
  • Radial sensors are less effective and stabilize lower range of N
  • Poloidal sensors stabilize the whole computed range of N

Poloidal Sensor

C = 10%

Radial Sensor Less Effective

Im[P(j)]

Im[P(j)]

22%

C-Coils

38%

67%

82%

-1

Re[P(j)]

Re[P(j)]

-1

Feedback Workshop, Austin

feedback modeling shows internal i coils are more effective than external c coils
I-Coils couple more effectively to the unstable RWM since closer to plasma

EIand EC are elements of excitation matrix

FEEDBACK MODELING SHOWS INTERNAL I-COILS ARE MORE EFFECTIVE THAN EXTERNAL C-COILS

Ratio of Effectiveness

C-coil / I-coil

I-Coils

5.0

EI / EC

2.5

C-Coils

0.0

0.0

0.5

1.0

I-Coils

C

Feedback Workshop, Austin

coupling of feedback coil to stable modes impedes stabilization
COUPLING OF FEEDBACK COIL TO STABLE MODES IMPEDES STABILIZATION

Nyquist Diagram

Ri

f Ri for all stable modes

f=1

C=42%

C=83%

f=3/4

f=1

f=1/2

f=3/4

f=1/4

f=1/2

f=1/4

f=1/8

f=1/16

(-1,0)

(-1,0)

Feedback Workshop, Austin

for real system the time constant of the external circuit is important
FOR REAL SYSTEM THE TIME CONSTANT OF THE EXTERNAL CIRCUIT IS IMPORTANT
  • Solution of characteristic equation

C=83%

c=.03 w

f=.15

f=1

30

RWM

Stable Modes

0

w

Circuit

-30

Voltage Amplification

Feedback Workshop, Austin

scoping study for c coil extensions
SCOPING STUDY FOR C-COIL EXTENSIONS

All Three Coils

  • Radial Sensor, Ideal Feedback

Upper

extension

1

30

C-Coil

Upper+ Lower

f

C-Coil

w

0

0

Lower extension

0

1

C

Feedback Workshop, Austin

summary conclusion
SUMMARY / CONCLUSION
  • Feedback with ideal plasma response formulated for general plasma equilibrium through energy conservation.
  • Phase space of feedback system reduced to the normal modes of open loop eigenfunctions and currents in feedback coils (NMA)
  • For tokamak geometry NMA has been implemented by coupling DCON with extended VACUUM to study RWM feedback stabilization
    • Poloidal sensors are more effective than radial sensors
    • I-Coils are more effective than C-coil
  • MARS-F benchmarked against NMA for ideal plasma

Feedback Workshop, Austin