space_charge

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space_charge

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{  SPACE_CHARGE.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.

 

 Adaptive grid refinement detects the space charge and refines

 the computation mesh to resolve its shape.

 

}  

 

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  

 r = sqrt(x^2+y^2)  

{ define the electrode center }  

 xc = sqrt((bigr-smallr)^2/2)  

 yc = xc  

{ A space charge source at -xc }  

 source = x/((x+xc)^2 + y^2 + 0.001)  

 k=0.1  

 

variables  

 V  

 

equations  

 V : 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  

 

plots  

grid(x,y)  

contour(V) as "Potential"  

contour(V) zoom(0.2,-0.2,0.4,0.4)  

surface(V) viewpoint (0,10,30)  

surface(V) zoom(-0.6,-0.2,0.4,0.4)  

surface(source) zoom(-0.6,-0.2,0.4,0.4)  

 

end