/src/utils/curlyh.m

function H=curlyh(b,a,n,np,l,theta,k1)



%  H=curlyH(b,a,n,np,l,theta,k1);

%

%  Computes <H> for normal boundary magnets per equation (20) of

%  SLAC-PUB-1193, "Evaluation of Synchrotron Radiation Integrals"

%

%  Inputs:

%

%     b     = beta at entrance of magnet [meter]

%     a     = alpha (= -b'/2) at entrance of magnet

%     n     = eta at entrance of magnet [meter]

%     np    = eta-prime at entrance of magnet

%     l     = length of magnet [meter]

%     theta = bend angle of magnet [radian]

%     k1    = quadrupole strength of magnet [1/meter^2]

%             (k1>0 for focusing, k1<0 for defocusing)



h=theta/l;

Ksq=h^2+k1;

if (Ksq<0)

   K=sqrt(-Ksq);

   Kl=K*l;

   C=cosh(Kl);

   S=sinh(Kl);

   sgn=-1;

else

   K=sqrt(Ksq);

   Kl=K*l;

   C=cos(Kl);

   S=sin(Kl);

   sgn=1;

end

g=(1+a^2)/b;



H=g*n^2+2*a*n*np+b*np^2 ...

 +sgn*2*l*h*(-(g*n+a*np)*(Kl-S)/(K*Kl^2)+(a*n+b*np)*(1-C)/(Kl^2)) ...

 +(l*h)^2*(g*(3*Kl-4*S+S*C)/(2*K^2*Kl^3)-a*(1-C)^2/(K*Kl^3) ...

 +sgn*b*(Kl-C*S)/(2*Kl^3));