| Author | Message | ||
     Philip (riche) Member Username: riche Post Number: 14 Registered: 06-2006 |
Hi Dr. Nelson In the following script ( problem 2,5D) in manual of Backstrom. Could you explain: 1)why we apply: value(Ephir) = 0 value(Ephii)= 0 at rotation axis ( I think that is Natural(Ephir)=0, Natural(Ephii)=0 in orde to conserve the flux) 2)why we need to multiply rad=sqrt(r^2+z^2) in the results (plot) Thank you very much TITLE { emw81.pde } 'Radiating Coil' SELECT errlim=1e-4 ngrid= 30 regrid= off vandenberg= on v216integral COORDINATES ycylinder('r','z') VARIABLES Ephir Ephii DEFINITIONS r0= 0.5e-3 r1= 1.0 mu0= 4*pi*1e-7 mu= mu0 sigma= 0 I0= 1.0 eps0= 8.854e-12 eps= eps0 omega= 10e9 Jphi0r { Current density in coil } k= omega* sqrt( mu*eps) rad= sqrt( r^2+ z^2) #include 'emw_rz.pde' EQUATIONS drr(Ephir)+ 1/r*dr(Ephir)+ dzz(Ephir)+ (k^2-1/r^2)*Ephir= 0 drr(Ephii)+1/r*dr(Ephii)+ dzz(Ephii)+ (k^2-1/r^2)*Ephii- omega*mu*Jphi0r= 0 BOUNDARIES region 'vacuum' Jphi0r= 0 start(0,-r1) natural(Ephir) = k*Ephii natural(Ephii)= -k*Ephir arc(center= 0,0) to (r1,0) to (0,r1) value(Ephir) = 0 value(Ephii)= 0 line to finish region 'coil' Jphi0r= I0/(2*r0)^2 start(0,-r0) line to (2*r0,-r0) to (2*r0,r0) to (0,r0) to finish PLOTS contour( rad*Ephir) painted contour( rad*Ephii) painted fixed range(-5e-2,5e-2) elevation( rad*Ephir, rad*Ephii) from (r1/20,0) to (r1,0) vector( Br) norm END 48907 { emw_rz.pde} Jphir= sigma*Ephir Jphii= sigma*Ephii Ep= sqrt( Ephir^2+ Ephii^2) Brhor= 1/omega*dz( Ephii) Brhoi= -1 /omega*dz( Ephir) Bzr= -1/(omega*r)* dr( r*Ephii) Bzi= 1/(omega*r)* dr( r*Ephir) Br= vector( Brhor, Bzr) Bi= vector( Brhoi, Bzi) Brm= magnitude( Br) Bim= magnitude( Bi) | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 755 Registered: 06-2003 |
1) I don't know. Apparently he believes the field to be zero on the axis. Perhaps he explains it in his book. See the link to his site on www.pdesolutions.com/bookstore.html 2) The plot drops rapidly with r, so to allow you to see the data at all r, he multiplies by r. Otherwise, you would see a sharp drop and a long tail of zero. |