1. 托卡马克的平衡计算 李国强 2013.12.18 四室学术报告

2. Introduction Decompose the physics problem by the orders (time order and space order) Traditional decomposition of plasma physics (by time order): equilibrium, stability and transport Equilibrium is the basis for other problem Here the equilibrium means the state of force equilibrium

3. Introduction (cont.)

4. Equilibrium and poloidal field coils Poloidal field coils induct the ohmic plasma current and control the plasma shape On EAST PF1-PF6, center solenoid, mainly for the ohmic current PF7/9, elongation PF11,PF13, trianglarity PF5, PF7/9, PF11, divertor control EAST PF coils and plasma configuration

5. Properties of equilibrium

6. Fixed boundary and free boundary equilibrium calculation Fixed boundary The plasma boundary is given, only calculate the plasma configuration inside the plasma Easy to calculate, useful for theory study Free boundary To calculate the configuration outside the plasma boundary The current in the PF coils is given Complicate but sometimes necessary A third kind Prescribe a non-fixed plasma boundary

7. Coordinate system Mesh in (R,z) coordinate R z

8. Coordinate system (cont.) Mesh in flux surface coordinate

9. Equilibrium construction and reconstruction Construction Generate an equilibrium from given profiles, plasma shape or current in PF coils, and other parameters Basis for tokamak design Basis for many theory study Reconstruction Find the experimental equilibrium from the diagnostic data Basis for experiments analysis

10. Equilibrium reconstruction with EFIT

11. Different EFIT reconstruction constraints DiagnosticsConstraintsYield Magnetic Magnetic loops and probes Ip, poloidal flux, external magnetic field Plasma current, plasma shape, internal inductance, betap, edge current profile Current Motional Stark Effect or Li Beam, SXR… Internal magnetic field or flux surface Magnetic surface, current profile, safety factor profile Kinetic Thomson scattering, ECE, CER, XCS, FADI, nubeam calculation… Pressure profile (from Te, Ti, ne, Zeff, Pf profiles) Pressure profile At present, EAST only has the magnetic diagnostics and limited kinetic diagnostics But we can add some constraints to the current profile

12. Magnetic diagnostic constraints All kinks of magnetic probe and flux loops Strait (2007)

13. kinetic profiles on EAST Data and fitting profiles for 38300.3900

14. Edge current constraint for H-mode plasma Typical pressure and current profiles of H-mode plasma at edge region Bootstrap current at the edge region EAST 38300, 3900ms

15. Kinetic equilibrium reconstruction on EAST With the constrains of magnetic diagnostics, pressure profile, edge current profile, we achieved the kinetic equilibrium The current/q profiles at the central region are not reliable, though we have the global li constrain 38300, 3900ms Pressure, current profiles and configuration from kinetic EFIT and magnetic EFIT

16. Equilibrium construction

17. Construct self-consistent equilibrium To construct a self-consistent equilibrium, the self-consistent plasma shape and profiles must be given Self-consistent profiles: Bootstrap current dominated edge current Self-consistent pedestal height and width, EPED model EPED model (peeling-ballooning model + kinetic ballooning model, ELITE+BALOO) has successfully predict the pedestal height and width This technic could be useful for EAST and CFETR

18. Thank you