linear_chromatic_tracking_setup

• type: setup command.
• function: define chromatic variation of beta functions, tunes, etc. for using in fast linear-chromatic tracking

&linear_chromatic_tracking_setup
    double nux[4] = {-1, 0, 0, 0};
    double betax[2] = {1.0, 0.0};
    double alphax[2] = {0.0, 0.0};
    double etax[2] = {0.0, 0.0};
    double etapx[2] = {0.0, 0.0};
    double nuy[4] = {-1, 0, 0, 0};
    double betay[2] = {1.0, 0.0};
    double alphay[2] = {0.0, 0.0};
    double etay[2] = {0.0, 0.0};
    double etapy[2] = {0.0, 0.0};
    double alphac[2] = {0.0, 0.0};
&end

• nux -- Provide the horizontal tune plus its first three chromatic derivatives, i.e., $\partial \nu_x/\partial\delta$, $\partial^2 \nu_x/\partial\delta^2$, and $\partial^3 \nu_x/\partial\delta^3$.
• betax -- Provide the horizontal beta function plus its chromatic derivative.
• alphax -- Provide the horizontal alpha function plus its chromatic derivative.
• etax -- Provide the first- and second-order horizontal dispersion: $\eta_x = \eta_x\left[0\right] + \eta_x\left[1\right]\delta$.
• etapx -- Provide the first- and second-order horizontal dispersion slope.
• alphac -- Provide the first and second-order momentum compaction. N.B: if you are tracking with an rf cavity, be sure that your lattice length equal to the actual circumference. See the example below.

An example of a good lattice for use with this feature is the following:

! Actual length of the ring
d0: drift,l=30.6667
! Actual rf voltage and frequency
rf: rfca,l=0,volt=30e3,phase=180,freq="c_mks 30.6667 /"
w1: watch,filename="%s.w1",mode="centroid"
ring: line=(d0,rf,w1)

Any additional elements (e.g,. wakes or impedances) should follow d0. No other elements represented by a matrix should be present!

An alternative for using this command is to use ILMATRIX elements in the lattice definition. This is more flexible, since one can include tune shifts with amplitude.