This function solves the dispersion relation and the wave equation
in the linear kinetic plasma model. It calculates the perpendicular index of
refraction and the polarization as a function of the wave
frequency and the parallel index of refraction.
- (x,y,z): We assume that the magnetic field is in the z direction and the
perpendicular index of refraction in the x direction.
- (p,m,z): p and m refer to the left hand and right hand rotating fields
respectively.
- (p,y,k): p and y are the transverse components of the polarization, with
respect to the wave vector. k is the longitudinal component.
INPUTS:
- Npar: parallel index of refraction [1,1]
- omega_rf: wave frequency (rad/s) [1,1]
- Te: electron temperature (keV) [1,1]
- ne: electron density (m-3) [1,1]
- zTi: ion temperature (keV) [1,i]
- zni: ion density (m-3) [1,i]
- zZi: ion charges [1,i]
- zmi: ion masses (mp) [1,i]
- Bfield: magnetic field amplitude [1,1]
- Nperp_in: perpendicular index of refraction (initial guess) [1,1] (default:1)
- herm_mode: mode for the calculation (0) full dielectric tensor, (1) hermitian part (default:0)
>>> In the case herm_mode = 1, the power flow and linear absorption
are also calculated
- display_mode: (0,1) none (2) convergence figures (default:0)
- nmax: maximum harmonic number (default:10)
- NZ: number of grid points in Z function integration calculation (default:100)
- tol: tolerance on the value of the dispersion relation (default:1e-6)
- method_type: 'newton', 'segments' (default:'newton')
OUTPUTS:
- Nperp: perpendicular index of refraction [1,1]
- e_xyz: polarization vector in the (x,y,z) coordinates [3,1]
- e_pmz: polarization vector in the (p,m,z) coordinates [3,1]
- e_pyk: polarization vector in the (p,y,k) coordinates [3,1]
- X: kinetic plasma susceptibility tensor elements [3,3]
- X_s: kinetic plasma susceptibility tensor elements for species s [3,3,1+i]
- X_sn: kinetic plasma susceptibility tensor elements for species s and harmonic n [3,3,1+i,N]
created 05/02/2003
by Joan Decker <jodecker@alum.mit.edu> (MIT/RLE) and Yves Peysson <yves.peysson@cea.fr> (CEA/DRFC)0001 function [Nperp,e_xyz,e_pmz,e_pyk,D,X,X_s,X_sn,alphaphi_lin,phiT_xyz,phiP_xyz,phiT_pmz,phiP_pmz,phiT_pyk,phiP_pyk]... 0002 = hotdisp_dke_jd(Npar,omega_rf,Te,ne,zTi,zni,zZi,zmi,Bfield,Nperp_in,herm_mode,display_mode,nmax,NZ,tol,method_type) 0003 % This function solves the dispersion relation and the wave equation 0004 % in the linear kinetic plasma model. It calculates the perpendicular index of 0005 % refraction and the polarization as a function of the wave 0006 % frequency and the parallel index of refraction. 0007 % 0008 % - (x,y,z): We assume that the magnetic field is in the z direction and the 0009 % perpendicular index of refraction in the x direction. 0010 % - (p,m,z): p and m refer to the left hand and right hand rotating fields 0011 % respectively. 0012 % - (p,y,k): p and y are the transverse components of the polarization, with 0013 % respect to the wave vector. k is the longitudinal component. 0014 % 0015 % INPUTS: 0016 % 0017 % - Npar: parallel index of refraction [1,1] 0018 % - omega_rf: wave frequency (rad/s) [1,1] 0019 % - Te: electron temperature (keV) [1,1] 0020 % - ne: electron density (m-3) [1,1] 0021 % - zTi: ion temperature (keV) [1,i] 0022 % - zni: ion density (m-3) [1,i] 0023 % - zZi: ion charges [1,i] 0024 % - zmi: ion masses (mp) [1,i] 0025 % - Bfield: magnetic field amplitude [1,1] 0026 % - Nperp_in: perpendicular index of refraction (initial guess) [1,1] (default:1) 0027 % - herm_mode: mode for the calculation (0) full dielectric tensor, (1) hermitian part (default:0) 0028 % >>> In the case herm_mode = 1, the power flow and linear absorption 0029 % are also calculated 0030 % - display_mode: (0,1) none (2) convergence figures (default:0) 0031 % - nmax: maximum harmonic number (default:10) 0032 % - NZ: number of grid points in Z function integration calculation (default:100) 0033 % - tol: tolerance on the value of the dispersion relation (default:1e-6) 0034 % - method_type: 'newton', 'segments' (default:'newton') 0035 % 0036 % OUTPUTS: 0037 % 0038 % - Nperp: perpendicular index of refraction [1,1] 0039 % - e_xyz: polarization vector in the (x,y,z) coordinates [3,1] 0040 % - e_pmz: polarization vector in the (p,m,z) coordinates [3,1] 0041 % - e_pyk: polarization vector in the (p,y,k) coordinates [3,1] 0042 % - X: kinetic plasma susceptibility tensor elements [3,3] 0043 % - X_s: kinetic plasma susceptibility tensor elements for species s [3,3,1+i] 0044 % - X_sn: kinetic plasma susceptibility tensor elements for species s and harmonic n [3,3,1+i,N] 0045 % 0046 % created 05/02/2003 0047 % by Joan Decker <jodecker@alum.mit.edu> (MIT/RLE) and Yves Peysson <yves.peysson@cea.fr> (CEA/DRFC) 0048 % 0049 if nargin < 16, 0050 method_type = 'newton'; 0051 end 0052 if nargin < 15, 0053 tol = 1e-5; 0054 end 0055 if nargin < 14, 0056 NZ = 1000; 0057 end 0058 if nargin < 13, 0059 nmax = 10; 0060 end 0061 if nargin < 12, 0062 display_mode = 0; 0063 end 0064 if nargin < 11, 0065 herm_mode = 0; 0066 end 0067 if nargin < 10, 0068 Nperp_in = 1.0; 0069 end 0070 % 0071 [qe,me,mp,mn,e0,mu0,re,mc2,clum] = pc_dke_yp; 0072 % 0073 ns = [ne;zni(:)]; 0074 qs = qe*[-1;zZi(:)]; 0075 ms = [me;mp*zmi(:)]; 0076 % 0077 wps = sqrt(ns.*qs.^2/e0./ms); 0078 wcs = qs*Bfield./ms; 0079 % 0080 ps = wps/omega_rf; 0081 ys = wcs/omega_rf; 0082 % 0083 bTs = sqrt([Te*1e3*qe/me/clum^2;zTi(:)*1e3*qe./(mp*zmi(:))/clum^2]); 0084 % 0085 [Nperp,e_xyz,e_pmz,e_pyk,D,X,X_s,X_sn,... 0086 alphaphi_lin,phiT_xyz,phiP_xyz,phiT_pmz,phiP_pmz,phiT_pyk,phiP_pyk]... 0087 = kineticdisp_jd(ps.^2,ys,bTs,Npar,Nperp_in,herm_mode,display_mode,nmax,NZ,tol,method_type); 0088 %