source: PSPA/parmelaPSPA/trunk/cathod.f @ 447

      real function cathod(rsq)
c        calculate the cathode shape z(rsq,ajones) according to Jones
c        IEEE NS-32, 1794 (1985)
c----------------------------------------------------------------------
c
      include 'param_sz.h'
c
      common/jones/ajones,zjones,zcath(imaa)
      real ajones,zjones,zcath
c----------------------------------------------------------------------
c        use units such that z = 1 at the zero-field point
      rrsq = rsq/zjones**2
      p3 = -ajones
      p = 3.*p3
      q = -3. + 6.*ajones - 1.5*rrsq
      r = 1.5*ajones*rrsq
      a = (3.*q - p**2)/3.
      b = (2.*p*p**2 - 9.*p*q + 27.*r)/27.
      const = a*a**2/27.
      surd = 0.25*b**2 + const
      cathod = 0.
      if (surd.ge.0.) then
        root = sqrt(surd)
        aa = -0.5*b + root
        sign = 1.
        if (aa.lt.0) then
          sign = -1.
          aa = -aa
        endif
        aa = sign*aa**.333333
        bb = -0.5*b - root
       sign = 1.
       if (bb.lt.0) then
          sign = -1.
          bb = -bb
        endif
        bb = sign*bb**.333333
        cathod = aa + bb - p3
      else
        phi = acos(-0.5*b/sqrt(-const))/3.
        fact = 2.*sqrt(-a/3.)
c        c1 = fact*cos(phi) - p3
c        c2 = fact*cos(phi + 2.094395) - p3
c          it appears that the 3rd root is the desired one
        cathod = fact*cos(phi + 4.188790) - p3
      endif
      cathod = cathod*zjones
      return
      end
c++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++*