sign of b1 multipole in quad (sextu..) wrong?

[lnadolski]

Dear All

I am facing something strange.
I set b1 to some value in a quad (or sextupole).
The orbit generated is of opposite sign of what is expected.
In the vertical plane this is fine.

I add the testing code using ESRF lattice.

Please let me know if you confirm the bug or if I am doing something wrong.

%% ESRF Lattice
Ring=esrf;

[LinData,nu, ksi] = atlinopt(Ring,0,1:length(Ring)+1)
beta = cat(1,LinData.beta);
phase= cat(1,LinData.mu);
eta = cat(2,LinData.Dispersion)';
spos = cat(1,LinData.SPos);

Id = 6;
theta = 1e-4;
orb_ana = (sqrt(beta(Id,1)beta(:,1))/2/sin(pinu(1)).cos(abs(phase(Id,1)-phase(:,1))-pinu(1))-eta(Id,1)*eta(:,1)/mcf(Ring)/LinData(end).SPos)*theta;

Ring{Id}.PolynomB(1)=theta/Ring{Id}.Length;

cod = getcod(Ring);
cod = cod';

figure(400)
clf
subplot(2,1,1)
plot(spos, orb_ana); hold all;
plot(spos, cod(:,1),'k*');
legend('Analytical', 'AT')
ylabel('horizontal orbit')

orb_ana2 = (sqrt(beta(Id,2)beta(:,2))/2/sin(pinu(2)).cos(abs(phase(Id,2)-phase(:,2))-pinu(2))-eta(Id,3)*eta(:,3)/mcf(Ring)/LinData(end).SPos)*theta;

Ring=esrf;
Ring{Id}.PolynomA(1)=theta/Ring{Id}.Length;

cod = getcod(Ring);
cod2 = cod';

subplot(2,1,2)
plot(spos, orb_ana2); hold all;
plot(spos, cod2(:,3),'k*');
legend('Analytical', 'AT')
ylabel('vertical orbit')

[carmignani]

Hello, the sign convention is different in horizontal and vertical in AT.
A positive PolynomA(1) gives a positive kick in y', a positive PolynomB(1) gives a negative kick in x'.

This is a piece of code from driftkick.c, where there is a minus sign where the horizontal kick is applied.

static void strthinkick(double* r, const double* A, const double* B, double L, int max_order)
/***************************************************************************** 
 Calculate and apply a multipole kick to a 6-dimentional
 phase space vector in a straight element (quadrupole)
 
 IMPORTANT !!!
 The reference coordinate system is straight but the field expansion may still
 contain dipole terms: PolynomA(1), PolynomB(1) - in MATLAB notation,
 A[0], B[0] - C,C++ notation
 
 ******************************************************************************/
{
   int i;
   double ReSum = B[max_order];
   double ImSum = A[max_order];
   double ReSumTemp;
   for (i=max_order-1; i>=0; i--) {
      ReSumTemp = ReSum*r[0] - ImSum*r[2] + B[i];
      ImSum = ImSum*r[0] +  ReSum*r[2] + A[i];
      ReSum = ReSumTemp;
   }
   r[1] -=  L*ReSum;
   r[3] +=  L*ImSum;
}

[lfarv]

This is not a bug but a consequence of the field expansion in AT. You can think of a “standard” bending magnet : it bends to the right (negative angle), while if you rotate it by 90 deg. It bends to the top (positive vertical angle). So definitely, as noted by @carmignani:
Positive B1 means negative H angle
Positive A1 means positive V angle