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280 lines (250 loc) · 7.37 KB
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%1d-3v的delta-f，静电code，试图解出带回旋运动的色散关系（国际单位制）
clear;
close all;
%% 参数设置
%物理参数
m=1.67e-27; %kg, 粒子质量
me=0.91e-30;
e=1.6e-19; %C,粒子电荷
epsilon0=8.854e-12; %F, 真空极化率
T0=150*e;%1500*e; %J,粒子温度乘以玻尔兹曼常数
v_th=sqrt(T0/m); %粒子热速度
n0=1e17;%1.0e19; %1/m^3,粒子密度
%B0=1.0; %T, 磁感应强度
%R0=1.0; %m, 长度单位，仅为与GTC单位对比使用
%phi0=1.0e-17*B0^2*R0^2*e/m; %V,外加驱动电势的大小
%omega=1.36911*e*B0/m;%1.54391*e*B0/m; %1/s，外加的波的频率
%x0=0.08660254;
%x1=0.1161895;
omegap=sqrt(n0*e^2/epsilon0/m);
omegape=sqrt(n0*e^2/epsilon0/me);
omegac=0.1*omegap;
B0=omegac*m/e;
omegace=e*B0/me;
k=0.7/(m*v_th/e/B0);% 波动的波数
lambdaD=sqrt(epsilon0*T0/(n0)/e^2);
rho0=n0*e/epsilon0;
L=4*pi/k;
x0=0;
x1=L+x0;
%程序参数
xgrids=127;%一维的空间格点
dx=L/xgrids;
xrange=x0:dx:x1; %空间范围
tstep=0.4/omegap;%0.5e-4*R0/v_th;%5.4143e-11;% %时间步长
mstep=5*ceil(2*pi/omegac/tstep)
micell=300;
mi=xgrids*micell; % marker数目
deltan=zeros(1,xgrids); %扰动的粒子密度
deltaE=zeros(1,xgrids); %扰动电场
poissonE=zeros(xgrids,1); %解poisson方程解出的扰动电场
nonlinear=1;
%诊断量
Etime=zeros(xgrids,mstep);
gyro_phi=zeros(xgrids,mstep);
ntime=zeros(xgrids,mstep);
parray=[1:mi 1:mi];
gk_phi_old = zeros(xgrids, mstep);
gk_phi_new = zeros(xgrids, mstep);
rhos = m*v_th/e/B0;
%% 粒子初始化
%rng('default'); %随机数种子设为default，每次运行结果相同，注释掉则以时间为种子
xp=linspace(x0,x1,mi)';%rand(1,mi)'*(x1-x0)+x0;% %粒子位置，均匀随机分布%
% xp=0.01*L*cos(k*xp)+xp; %初始扰动
vpx=v_th*randn(mi,1);%normrnd(0.0,v_th,[mi,1]);%粒子速度，玻尔兹曼分布,注意与GTC的差别？
vpy=v_th*randn(mi,1);%normrnd(0.0,v_th,[mi,1]);
vpz=v_th*randn(mi,1);%normrnd(0.0,v_th,[mi,1]);
vpx=max(-5*v_th,min(5*v_th,vpx));
vpy=max(-5*v_th,min(5*v_th,vpy));
vpz=max(-5*v_th,min(5*v_th,vpz));
rho_x=m*vpy/e/B0;
% xp=xp-rho_x;
pw=zeros(mi,1);
A=zeros(xgrids,xgrids);
for i=2:xgrids-1
A(i,i)=2/dx^2;
A(i,i-1)=-1/dx^2;
A(i,i+1)=-1/dx^2;
end
A(1,1)=2/dx^2;
A(1,2)=-1/dx^2;
A(1,xgrids)=-1/dx^2;
B=A;
A(end,:)=1;
A=A*n0*(m/B0^2);
B(end,1)=-1/dx^2;
B(end,end)=2/dx^2;
B(end,end-1)=-1/dx^2;
C=B;
B=B*lambdaD^2;
B(end,:)=1;
Diff=zeros(xgrids);
for i=2:xgrids-1
Diff(i,i+1)=1/2/dx;
Diff(i,i-1)=-1/2/dx;
end
Diff(end,:) = 1;
Diff(1,1) = 1;
% Diff(1,2)=1/2/dx;
% Diff(1,end)=-1/2/dx;
% Diff(end,1)=1/2/dx;
% Diff(end,end-1)=-1/2/dx;
a=1;
psir = @(r) (r.^2/2)/1000;
psiw = 0.0375e-3;
psi0 = 0.1*psiw;
psi1 = 0.3*psiw;
rpsi = @(psi) sqrt(2*psi*1000);
rmesh = linspace(rpsi(psi0), rpsi(psi1), xgrids)';
ppsi = psir(xp / L * (rpsi(psi1) - rpsi(psi0)) + rpsi(psi0));
for i = 1:mi
if xp(i) > 0.5 * L
ppsi(i) = psir((1-xp(i) / L) * (rpsi(psi1) - rpsi(psi0)) + rpsi(psi0));
end
end
psimesh=psir(rmesh);
meshne = zeros(xgrids,1);
meshne(1:ceil(xgrids/2)) = 0.7 - tanh(((psimesh(1:ceil(xgrids/2))/psiw) - 0.15)*300)/4;
meshne(ceil(xgrids/2):xgrids) = meshne(ceil(xgrids/2):-1:1);
pw = pw+0.01*sin(k*xp);
% for i=1:mi
% pw(i) = pw(i) *( (0.7 - tanh((ppsi(i)/psiw - 0.12)*500)/4)/meshne(1));
% end
meshne = meshne / meshne(1);
meshni=meshne;
meshte=ones(xgrids,1);
meshti=meshte;
% rho0= rho0 * meshni';
%dr = rmesh(1) - rmesh(0);
Mdr = zeros(xgrids);
for i=2:xgrids - 1
Mdr(i,i+1)=0.5/dx;
Mdr(i,i-1)=-0.5/dx;
end
Mdr(1,end)=-0.5/dx;Mdr(1,2)=0.5/dx;
Mdr(end,1)=0.5/dx; Mdr(end, end-1) = -0.5/dx;
kapani=Mdr*meshni./meshni;
figure;subplot(211);plot(meshne);subplot(212);plot(rhos*kapani);
Mlap=zeros(xgrids);
for i=2:xgrids-1
Mlap(i,i)=-2/dx^2;
Mlap(i,i+1)=1/dx^2;
Mlap(i,i-1)=1/dx^2;
end
Mlap(1,1)=-2/dx^2;
Mlap(1,2)=1/dx^2;
Mlap(1,xgrids)=1/dx^2;
Mlap(end,end)=-2/dx^2;
Mlap(end,end-1) = 1/dx^2;
Mlap(end,1) = 1/dx^2;
Mlap_new = Mlap;
for i=1:xgrids
Mlap_new(i,:) = Mlap_new(i,:)+1*kapani(i)*Mdr(i,:);
end
Mold = Mlap;
for i=1:xgrids-1
Mold(i,:) = -Mold(i,:)*e^2*(n0*meshni(i))/epsilon0/(T0*meshti(i))*rhos^2;
end
Mold = diag(e^2*n0*meshne/epsilon0./(T0*meshte))+(eye(xgrids)-rhos^2*Mlap)\Mold-Mlap;
Mold(end,:)=1;
% Mold(1,:)=0;
% Mold(1,1)=1;
% Mold(end,:)=0;
% Mold(end,end)=1;
%Mlap_new=Mlap;
Mnew = Mlap_new;
for i=1:xgrids-1
Mnew(i,:) = -Mnew(i,:)*e^2*(n0*meshni(i))/epsilon0/(T0*meshti(i))*rhos^2;
end
Mnew = (eye(xgrids)- rhos^2*Mlap_new)\Mnew+diag(e^2*n0*meshne/epsilon0./(T0*meshte))-Mlap;
Mnew(end,:)=1;
% Mnew(1,:)=0;
% Mnew(1,1)=1;
% Mnew(end,:)=0;
% Mnew(end,end)=1;
B=Mlap-diag(e^2*n0*meshne/epsilon0./(T0*meshte));
B(end,:)=1;
% B(1,:)=0;
% B(1,1)=1;
% B(end,:)=0;
% B(end,end)=1;
%%
figure;
dtime=tstep;
for istep=1:mstep;
if(istep<=mstep)
extphi=1.0e4*sin(k*[dx/2:dx:L-dx/2]')*sin(0.06*omegac*tstep*istep);
else
extE=0.0;
end
xp=xp./L+10.0; xp=L.*(xp-floor(xp));
%push x
xp=xp+vpx*dtime;
% xp=mod(xp-x0,(x1-x0))+x0;%更新坐标，使用了周期性边界条件
xp=xp./L+10.0; xp=L.*(xp-floor(xp));
g0=floor(xp/dx-.5)+1;%floor((xp-x0)/dx-0.5)+1;
g=[g0;g0+1];
out=(g<1);g(out)=g(out)+xgrids;
out=(g>xgrids);g(out)=g(out)-xgrids;
h1=abs(xp/dx-g0+.5);%mod((xp-x0)/dx+0.5,1);
h=[1-h1;h1];
mat=sparse(parray,g,h,mi,xgrids);
rho=(pw'*mat)*n0/micell;
rho1=rho-mean(rho);
% rho1(1)=0;
rho1(end) = 0;
% phi = -B\(rho1' .* meshni);
%phi(end) = 1/2*(phi(end-1)+phi(1));
poissonE=-Mdr*extphi;
pw = pw+vpx.*(mat*poissonE)*e/T0*dtime;
%vpx=vpx+mat*poissonE*e/m*dtime/2;
gammab=e*B0/m*dtime/(1+e^2*B0^2/m^2/4*dtime^2);
vx1=vpx+(vpy-vpx*e*B0/m*dtime/2)*gammab;
vpy=vpy-(vpx+vpy*e*B0/m*dtime/2)*gammab;
vpx=vx1;
%vpx=vx1+mat*poissonE*e/m*dtime/2;
rho_x=m*vpy/e/B0;
rho_perp=m*sqrt(vpx.^2+vpy.^2)/e/B0;
gx=xp+rho_x;
gx_left=gx-rho_perp;
gx_right=gx+rho_perp;
g0=floor(gx/dx-.5)+1;%floor((xp-x0)/dx-0.5)+1;
g0_left=floor(gx_left/dx-.5)+1;
g0_right=floor(gx_right/dx-.5)+1;
g=[g0;g0+1];
g_left=[g0_left;g0_left+1];
g_right=[g0_right;g0_right+1];
out=(g<1);g(out)=g(out)+xgrids;
out_left=(g_left<1);g_left(out_left)=g_left(out_left)+xgrids;
out_right=(g_right<1);g_right(out_right)=g_right(out_right)+xgrids;
out=(g>xgrids);g(out)=g(out)-xgrids;
out_left=(g_left>xgrids);g_left(out_left)=g_left(out_left)-xgrids;
out_right=(g_right>xgrids);g_right(out_right)=g_right(out_right)-xgrids;
h1=abs(gx/dx-g0+.5);%mod((xp-x0)/dx+0.5,1);
h1_left=abs(gx_left/dx-g0_left+.5);
h1_right=abs(gx_right/dx-g0_right+.5);
h=[1-h1;h1];
h_left=[1-h1_left;h1];
h_right=[1-h1_right;h1];
mat=sparse(parray,g,h,mi,xgrids);
mat_left=sparse(parray,g_left,h_left,mi,xgrids);
mat_right=sparse(parray,g_right,h_right,mi,xgrids);
g_rho= + (pw'*mat)*n0/micell;%*0.5...
%+0.25*(e/epsilon0*(pw'*mat_left))*n0/micell*epsilon0...
%+0.25*(e/epsilon0*(pw'*mat_right))*n0/micell*epsilon0;%-rho0 * epsilon0;
g_rho=g_rho-mean(g_rho);
ntime(:,istep)=rho;
% end
subplot(2,2,1);
plot(dx/2:dx:L-dx/2,extphi);
title(['t=',num2str(istep)]);
subplot(2,2,2);plot(dx/2:dx:L-dx/2,rho);
subplot(2,2,3);plot(dx/2:dx:L-dx/2,g_rho);
subplot(2,2,4);plot(dx/2:dx:L-dx/2,g_rho-rho);
drawnow;
end
% figure;
% fE=fft(Etime(xgrids/2,:));
% ft=[1:mstep]/mstep*(2*pi/(omegac*dtime));
% plot(ft,abs(fE));
% xlim([0,10])