def drdpsiN_of_r(a,simul):
print "++++++++++++++++++++++++++++"
print "GENERATING PSI"
print "++++++++++++++++++++++++++++"
q95=simul.inputs.Miller_q
kappa90=simul.inputs.Miller_kappa
RBar=simul.RBar
BBar=simul.BBar
#rescale q_profile to fit whatever q95 we have in the simulation
scale_q=q95/3.5
scale_kappa=kappa90/1.58
#actual profile has q95~3.5
kappay=scale_kappa*numpy.array([1.23,1.37,1.58])
kappax=numpy.array([0,0.5,0.9])
deg=2
#in what follows, rho=r/a
kappa_rho=func_polyfit(kappax,kappay,deg) #kappa(rho)
dkappadrho=func_polyfit_derivative(kappax,kappay,deg) #dkappadrho(rho)
#generate the integrated B_T as function of minor radius of eliptical cross-section
BT_r=lambda x: simul.BBar*1.0/simul.inputs.RHat(0.0) #should be B_T(r), here taken as constant and at theta=0
dBTdr=lambda x: 0 #dBTdr(r)
#calculate radial derivative of toroidal flux Psi_T (assumes small theta dependence in B)
dPsiTdr=toroidal_flux_derivative(a,kappa_rho,dkappadrho,BT_r,dBTdr)
#calculate q profile
q_rho=func_q(1.0,3.5*scale_q,0.6,1.6*scale_q) #q(rho)
q_r=lambda r:q_rho(r/a) #q(rho=r/a)
if Verbose:
plotNum = 1
numRows = 1
numCols = 4
fig = plt.figure()
xp=numpy.linspace(0,1)
ax = fig.add_subplot(numRows, numCols, plotNum); plotNum += 1
ax.plot(xp, q_rho(xp))
ax = fig.add_subplot(numRows, numCols, plotNum); plotNum += 1
ax.plot(xp, kappa_rho(xp))
ax = fig.add_subplot(numRows, numCols, plotNum); plotNum += 1
ax.plot(xp, dPsiTdr(xp))
#calculate psi(r)
psi_r=func_psi(q_r,dPsiTdr) #psi(r), will be in the same units as BBar and RBar
psiAHat=psi_r(a)/(BBar*RBar**2) #translates to/from unitless psi to psi_N
simul.inputs.changevar("physicsParameters","psiAHat",psiAHat)
simul.inputs.read(simul.input_filename)
#print drdPsiN_at_psiN_one(q_r,dPsiTdr,psi_r,a)
if Verbose:
print drdPsiN_at_psiN_one(q_r,dPsiTdr,psi_r,a)[0]
ax = fig.add_subplot(numRows, numCols, plotNum); plotNum += 1
xr=numpy.linspace(0.1,0.7)
psi_array=[psi_r(xxx) for xxx in xr]
ax.plot(xr,psi_array)
plt.show()
return drdPsiN_at_psiN_one(q_r,dPsiTdr,psi_r,a)[0]
def psi_pedestal_width(deltar, q, dPsiTdr, psi, r_ped):
drdpsi = drdPsiN_at_psiN_one(q, dPsiTdr, psi, r_ped)[0]
return deltar / drdpsi
if __name__ == "__main__":
y = numpy.array([1.23, 1.37, 1.6])
x = numpy.array([0, 0.5, 0.9])
# flat profile
# y=numpy.array([1.73,1.73,1.73])
# x=numpy.array([0,0.5,0.9])
deg = 2
kappa = func_polyfit(x, y, deg)
dkappadrho = func_polyfit_derivative(x, y, deg)
q_of_rho = func_q(1.0, 3.5, 0.6, 1.6)
# flat profile
# q=func_q(3.5,3.5,0.6,3.5)
# does not actually matter in psiN since its normalized away
# would matter if we calculated psi(r)
BT = lambda x: 2.93 # Value for the average BT, taken from BBar in T for JETLike profile
dBTdr = lambda x: 0
N = 100
rmin = 0
rmax = 0.7
q = lambda r: q_of_rho(r / rmax)
dPsiTdr = toroidal_flux_derivative(rmax, kappa, dkappadrho, BT, dBTdr)
psi = func_psi(q, dPsiTdr)
r = numpy.linspace(rmin, rmax, N)