The PTC_NORMAL module of MAD-X [a,b] is based on PTC code. This module takes full advantage of the PTC Normal Form analysis which is a considerable upgrade of what was available with the Lie Algebra technique used in MAD8. It allows to calculate dispersions, chromaticities, anharmonicities and Hamiltonian terms to very high order. In fact, the order is only limited by the RAM memory of your computer and your patience to wait for the results.
The number of terms per order increases with some power law. The internal MAD-X tables are not adequate to keep such large amounts of data. On the other hand, only a reduced set of this data is actually needed by the user. Thus a much easier and flexible solution is to gather the users requirements with a series of special MAD-X command called SELECT_PTC_NORMAL. A special MAD-X table is dynamically built using just those commands and it will be filled by the next call to the PTC_NORMAL-command.
Another essential advantage of this table is the fact that it is structured to facilitate exchange of Normal Form (including Hamiltonian terms of high order) between MAD-X modules. The immediate goal is to use this table to allow non-linear matching inside the present MAD-X MATCHING module.
PTC_CREATE_UNIVERSE;
PTC_CREATE_LAYOUT, model=integer,method=integer,
nst=integer, [exact];
..............................
SELECT_PTC_NORMAL, dx,..., gnfu;
..............................
PTC_NORMAL;
WRITE, table=normal_results, file=normal_results;
..............................
PTC_END;
Notation | Meaning | Value |
---|---|---|
DX, DPX, DY,DPY |
dispersions, Dx(n), Dpx(n),
Dy(n), Dpy(n) |
n |
Q1, Q2 |
horizontal and vertical |
0 |
DQ1, DQ2 | derivatives of horizontal and vertical tunes ∂(n)q1/∂δp(n), ∂(n)q2/∂δp(n) |
n |
ANHX, ANHY | Anharmonicities |
n(ε1),
n(ε2),
|
GNFU | Generating Function |
n, 0, 0 |
HAML | Hamiltonian |
n, 0, 0 |
EIGN | Eigenvector (the n2-th
component of the n1-th eigenvector) |
n1, n2 |
Option | Meaning | Default Value | Value Type |
---|---|---|---|
ICASE | the user-defined dimensionality
of the phase-space (4, 5 or 6) |
4 |
integer |
NO | the order of the map. |
1 |
integer |
CLOSED_ORBIT | the switch to turn on the closed orbit calculation. |
.FALSE. |
logical |
DELTAP |
relative momentum offset |
0.0 |
double |
MAPTABLE | turn on the map-table in memory |
.FALSE. |
logical |
NORMAL | turn on the calculation of the Normal Form |
.FALSE. |
logical |
MAPTABLE: (requires no=1) creates the one-turn matrix which can be used by the next PTC_TWISS command.