quantumDiff

quantumDiff    Compute the radiation-diffusion matrix

DIFFMAT=QUANTUMDIFF(RING,RADINDEX)

   RING:       Closed ring AT structure, containing radiative elements and
               RF cavity
   RADINDEX:   Indices of elements where diffusion occurs, typically dipoles
               and quadrupoles.

DIFFMAT=QUANTUMDIFF(ELEMS,RADINDEX,ORBIT0)

   ELEMS:      AT structure
   RADINDEX:   Indices of elements where diffusion occurs, typically dipoles
               and quadrupoles.
   ORBIT0:     Initial 6-D closed orbit

 In this mode, ELEMS may be a section of a ring

0001 function DiffMat = quantumDiff(elems,radindex,orb0)
0002 %quantumDiff    Compute the radiation-diffusion matrix
0003 %
0004 %DIFFMAT=QUANTUMDIFF(RING,RADINDEX)
0005 %
0006 %   RING:       Closed ring AT structure, containing radiative elements and
0007 %               RF cavity
0008 %   RADINDEX:   Indices of elements where diffusion occurs, typically dipoles
0009 %               and quadrupoles.
0010 %
0011 %DIFFMAT=QUANTUMDIFF(ELEMS,RADINDEX,ORBIT0)
0012 %
0013 %   ELEMS:      AT structure
0014 %   RADINDEX:   Indices of elements where diffusion occurs, typically dipoles
0015 %               and quadrupoles.
0016 %   ORBIT0:     Initial 6-D closed orbit
0017 %
0018 % In this mode, ELEMS may be a section of a ring
0019 
0020 NumElements=length(elems);
0021 
0022 %[mring, ms, orbit] = findm66(ring,1:NumElements+1);
0023 if (nargin >= 3)
0024     orb=num2cell(linepass(elems, orb0, 1:NumElements),1)';
0025 else
0026     orb=num2cell(findorbit6(elems, 1:NumElements),1)';
0027 end
0028 
0029 zr={zeros(6,6)};
0030 B=zr(ones(NumElements,1));   % B{i} is the diffusion matrix of the i-th element
0031 
0032 % calculate Radiation-Diffusion matrix B for elements with radiation
0033 B(radindex)=cellfun(@findmpoleraddiffmatrix,...
0034     elems(radindex),orb(radindex),'UniformOutput',false);
0035 
0036 % Calculate cumulative Radiation-Diffusion matrix for the ring
0037 BCUM = zeros(6,6);
0038 % Batbeg{i} is the cumulative diffusion matrix from
0039 % 0 to the beginning of the i-th element
0040 Batbeg=[zr;cellfun(@cumulb,elems,orb,B,'UniformOutput',false)]; %#ok<NASGU>
0041 
0042 DiffCum = BCUM;
0043 
0044 DiffMat=(DiffCum+DiffCum')/2;
0045 
0046 %Lmat=chol((DiffCum+DiffCum')/2);
0047 
0048  function btx=cumulb(elem,orbit,b)
0049         % Calculate 6-by-6 linear transfer matrix in each element
0050         % near the equilibrium orbit
0051         m=findelemm66(elem,elem.PassMethod,orbit);
0052         % Cumulative diffusion matrix of the entire ring
0053         BCUM = m*BCUM*m' + b;
0054         btx=BCUM;
0055  end
0056 end
0057