geometry Module

Deals with most types of equilibria to generate GS2's expected geometrical parameters Input: rhoc :: minor radius of surface of interest (see irho below) use_large_aspect :: default false. Choose true to get "s-alpha" equilibria (see local_eq) Equilibrium options : Choose 1 of: local_eq : Analytic parameterization of local equilibrium ppl_eq = .true. :: use PPL style NetCDF equilibrium (Menard) transp_eq = .true. :: use TRXPL style NetCDF equilibrium (Menard) gen_eq = .true. :: use GA style NetCDF equilibrium (TOQ) chs_eq = .true. :: Use CHEASE generated equilibrium efit_eq = .true. :: use EFIT equilibrium dfit_eq = .true. :: use dipole equilibrium -------------------> [note: if any of the above except local_eq are true set eqfile = input file name] irho :: choose flux surface label case (1) :: sqrt(toroidal flux)/sqrt(toroidal flux of LCFS) case (2) :: diameter/(diameter of LCFS). recommended case (3) :: poloidal flux/(poloidal flux of LCFS) case (4) :: rho_mid? Only used for the vacuum ring dipole, dfit_eq = T

equal_arc :: .true. makes grad_par coefficient a constant.

New feature: Given an actual equilibrium, allow s_hat and d pressure/d rho to vary self-consistently (a la Greene and Chance, Bishop). We use the Bishop formalism [C. M. Bishop, et al., NF, Vol. 24, 1579 (1984).]

bishop :: uses Bishop relations to generate coefficients. case(0) :: do not use Bishop relations -- primarily for testing case(1) :: use Bishop relations with actual equilibrium shat, p' case(2) :: use Bishop relations with new shat, and p' from p_prime_input case(3) :: use Bishop relations with new shat, L_p from below s_hat_input :: new magnetic shear, rho/qdq/drho invLp_input :: new -1/pressure * d pressure/d rho case(4) :: use Bishop relations with new shat, beta' from below s_hat_input :: new magnetic shear, rho/qdq/drho beta_prime_input :: new d beta/d rho case(5) :: use Bishop relations with new shat, alpha from below s_hat_input :: new magnetic shear, rho/qdq/drho alpha_input :: new alpha = -q*2 * rmaj * d pressure/d rho case(6) :: use Bishop relations with equilibrium shat, beta' from below beta_prime_input :: new d beta/d rho case(7) :: use Bishop relations with equilibrium shat, beta' from below dp_mult :: d pressure/d rho = equilibrium gradient * dp_mult (In each case, the definition of rho is determined by irho above)

nperiod :: number of cells of width 2 pi in theta.

geoType :: determines the analytic geometry specification case (0) :: the tilted Miller geometry: generalization of Miller et al. PoP 1998 (see Chapter 3.2.1 of J. Ball MIT Masters thesis) case (1) :: the global MHD solution geometry: calculated by inverting the large aspect ratio, constant-current MHD solution (see J. Ball "Optimized up-down asymmetry to drive fast intrinsic rotation in tokamak reactors") case (2) :: the generalized ellipticity geometry: the polar formula for an ellipse generalized to arbitrary shaping effect mode number (see Chapter 5.1.2 of J. Ball Oxford PhD thesis) case (3) :: the Fourier series geometry: Fourier decomposition of the minor radius as a function of poloidal angle (see Chapter 5.1.1 of J. Ball Oxford PhD thesis) rmaj :: major radius of magnetic axis (in units of aminor) if not local_eq or major radius of center of flux surface of interest (units of aminor) otherwise r_geo :: major radius of last closed flux surface or if local_eq: sets the reference magnetic field to be the value of the toroidal field at R=r_geo on the flux surface of interest aSurf :: the real-space flux surface label of the surface with deltam and deltan shaping as well as a major radius of Rmaj (only used when geoType={1}) shift :: d rmaj/drho. (Typically < 0.) (only used when geoType={0,2,3}) -> Alternative definitions: Raxis :: major radial location of the magnetic axis. (only used when geoType={1}) shiftVert :: d zmaj/drho. (< 0 for a vertical shift) (only used when geoType={0,2,3}) -> Alternative definitions: Zaxis :: axial location of the magnetic axis. (only used when geoType={1}) mMode :: the first poloidal mode number (only used when geoType={2,3}) nMode :: the second poloidal mode number (only used when geoType={2,3}) deltam :: magnitude of the first poloidal shaping effect (only used when geoType={2,3}) -> Alternative definitions: delta2 :: identical to akappa (only used when geoType={1}) akappa :: flux surface elongation (only used when geoType={0}) deltan :: magnitude of the second poloidal shaping effect (only used when geoType={2,3}) -> Alternative definitions: delta3 :: magnitude of the triangulaity-like shaping effect (only used when geoType={1}) tri :: flux surface triangulaity (only used when geoType={0}) deltampri :: d(deltam)/d(rhoc) (only used when geoType={2,3}) -> Alternative definitions: akappapri :: d(akappa)/d(rhoc) (only used when geoType={0}) deltanpri :: d(deltan)/d(rhoc) (only used when geoType={2,3}) -> Alternative definitions: tripri :: d(tri)/d(rhoc) (only used when geoType={0}) thetam :: tilt angle of the first poloidal shaping effect (only used when geoType={2,3}) -> Alternative definitions: theta2 :: tilt angle of the flux surface elongation (only used when geoType={1}) thetak :: tilt angle of the flux surface elongation (only used when geoType={0}) thetan :: tilt angle of the first poloidal shaping effect (only used when geoType={2,3}) -> Alternative definitions: theta3 :: tilt angle of the triangularity-like shaping effect (only used when geoType={1}) thetad :: tilt angle of the flux surface triangularity (only used when geoType={0}) qinp :: safety factor q at surface of interest (local_eq = T only) shat :: d q/drho at surface of interest

delrho :: numerical parameter. Should be "small enough". Typically 0.001 ok.

force_sym :: true -> assume up-down symmetric equilibrium. writelots :: .true. for more output

Use: Include this module, set input variables appropriately and call eikcoefs.

I do not recommend calling other routines, but a few are available for diagnostic purposes.