{ SPACECHARGE.PDE }
{
This problem describes the electric field in an insulated cardioid-like
chamber due to an electrode at the tip of the cardioid and a localized
space charge near the center of the body. }
title "Electrostatic Potential with probe and space charge"
select errlim = 1e-4
definitions
bigr = 1
smallr = 0.4
x0 = sqrt(bigr**2/2)
y0 = x0
xc = sqrt((bigr-smallr)**2/2)
yc = xc
r = sqrt(x^2+y^2)
source = (x/r)/((x+xc)**2 + y**2 + 0.0001)
k=0.1
variables
V
equations
div(k*grad(V)) + source = 0
boundaries
region 1
start(xc,yc-smallr)
natural(V) = 0 { -- insulated outer boundary }
arc(center=xc,yc) to (x0,y0)
arc(center=0,0) angle 270
arc(center=xc,-yc) to (xc,smallr-yc)
value(V)=1 { -- applied voltage = 1 on tip }
arc(center=xc,0) angle -180 to close
monitors
contour(V)
plots
grid(x,y)
contour(V) as "Potential"
contour(V) zoom(0.2,-0.2,0.4,0.4)
surface(V) viewpoint (0,1,30)
end