Qval

 Qval gives the unitless Q parameter needed to compute the
 bunch lengthening factor due to the potential well effect

0001 function Q = Qval(Ib,Zn,Vrf,U0,E0,h,alpha,sigdelta)
0002 % Qval gives the unitless Q parameter needed to compute the
0003 % bunch lengthening factor due to the potential well effect
0004 
0005 % Ib is the bunch current in mA
0006 % Zn is the longitudinal broadband impedance
0007 % Vrf is the RF voltage in MV
0008 % h is the harmonic number
0009 % alpha is the momentum compaction factor
0010 % sigmadelta is the energy spread
0011 % nus is the synchrotron tune
0012 
0013 phi=pi - asin(U0/Vrf);
0014 nus= sqrt(-(Vrf/E0)*(h * alpha)/(2*pi) * cos(phi));
0015 
0016 Delta = -(2*pi*Ib*Zn)/(Vrf*h*cos(phi)*(alpha*sigdelta/nus)^3);
0017 Q=Delta/(4*sqrt(pi));