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Fixes to exact drift when pt is large and beta << 1 #1077

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merged 2 commits into from Feb 25, 2022
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Fixes to exact drift when pt is large and beta << 1 #1077

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tpersson Feb 2, 2022
a22faf1
Imporved test and cleaned up.
tpersson Feb 2, 2022
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77 changes: 39 additions & 38 deletions src/twiss.f90
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Expand Up @@ -7139,7 +7139,7 @@ SUBROUTINE tmdrf(fsec,ftrk,orbit,fmap,dl,ek,re,te)
use twissbeamfi, only : beta, gamma, dtbyds
use twisslfi
use matrices, only : EYE
use math_constfi, only : zero, two, three
use math_constfi, only : zero, one, two, three
implicit none
!----------------------------------------------------------------------*
! Purpose: *
Expand Down Expand Up @@ -7172,54 +7172,55 @@ SUBROUTINE tmdrf(fsec,ftrk,orbit,fmap,dl,ek,re,te)
py = orbit(4)
pt = orbit(6)

csq = 1 + 2*pt*beta + pt**2 - px**2 - py**2
csq = 1 + 2*pt/beta + pt**2 - px**2 - py**2
l_pz = dl / sqrt(csq)
c3sq = csq**(3d0/2d0)
c52sq =csq**(5d0/2d0)
re(1,2) = dl/sqrt(csq) + dl*px**2/c3sq;
re(1,4) = dl*px*py/c3sq;
re(1,6) = dl*px*(-beta - pt)/c3sq;
re(3,2) = dl*px*py/c3sq;
re(3,4) = dl/sqrt(csq) + dl*py**2/c3sq;
re(3,6) = dl*py*(-beta - pt)/c3sq;
re(5,2) = -dl*px*(beta + pt)/c3sq;
re(5,4) = -dl*py*(beta + pt)/c3sq;
re(5,6) = -dl/sqrt(csq) - dl*(-beta - pt)*(beta + pt)/c3sq;

re(1,2) = dl/sqrt(csq) + dl*px**2/c3sq
re(1,4) = dl*px*py/c3sq
re(1,6) = dl*px*(-pt - 1d0/beta)/c3sq
re(3,2) = dl*px*py/c3sq
re(3,4) = dl/sqrt(csq) + dl*py**2/c3sq
re(3,6) = dl*py*(-pt - 1d0/beta)/c3sq
re(5,2) = -dl*px*(beta + pt)/c3sq
re(5,4) = -dl*py*(beta + pt)/c3sq
re(5,6) = -dl/sqrt(csq) - dl*(beta + pt)*(-pt - 1d0/beta)/c3sq

if (fsec) then
te(1,2,2) = 3d0*dl*px/(2d0*csq**(3d0/2d0)) + 3d0*dl*px**3d0/(2d0*c52sq)
te(1,2,4) = dl*py/(2d0*csq**(3d0/2d0)) + 3d0*dl*px**2d0*py/(2d0*c52sq)
te(1,2,6) = dl*(-beta - pt)/(2d0*csq**(3d0/2d0)) + dl*px**2d0*(-3d0*beta - 3d0*pt)/(2d0*c52sq)
te(1,4,2) = dl*py/(2d0*csq**(3d0/2d0)) + 3d0*dl*px**2d0*py/(2d0*c52sq)
te(1,4,4) = dl*px/(2d0*csq**(3d0/2d0)) + 3d0*dl*px*py**2d0/(2d0*c52sq)
te(1,4,6) = dl*px*py*(-3d0*beta - 3d0*pt)/(2d0*c52sq)
te(1,6,2) = dl*(-beta - pt)/(2d0*csq**(3d0/2d0)) + 3d0*dl*px**2d0*(-beta - pt)/(2d0*c52sq)
te(1,6,4) = 3d0*dl*px*py*(-beta - pt)/(2d0*c52sq)
te(1,6,6) = -dl*px/(2d0*csq**(3d0/2d0)) + dl*px*(-3d0*beta - 3d0*pt)*(-beta - pt)/(2d0*c52sq)
te(3,2,2) = dl*py/(2d0*csq**(3d0/2d0)) + 3d0*dl*px**2d0*py/(2d0*c52sq)
te(3,2,4) = dl*px/(2d0*csq**(3d0/2d0)) + 3d0*dl*px*py**2d0/(2d0*c52sq)
te(3,2,6) = dl*px*py*(-3d0*beta - 3d0*pt)/(2d0*c52sq)
te(3,4,2) = dl*px/(2d0*csq**(3d0/2d0)) + 3d0*dl*px*py**2d0/(2d0*c52sq)
te(3,4,4) = 3d0*dl*py/(2d0*csq**(3d0/2d0)) + 3d0*dl*py**3d0/(2d0*c52sq)
te(3,4,6) = dl*(-beta - pt)/(2d0*csq**(3d0/2d0)) + dl*py**2d0*(-3d0*beta - 3d0*pt)/(2d0*c52sq)
te(3,6,2) = 3d0*dl*px*py*(-beta - pt)/(2d0*c52sq)
te(3,6,4) = dl*(-beta - pt)/(2d0*csq**(3d0/2d0)) + 3d0*dl*py**2d0*(-beta - pt)/(2d0*c52sq)
te(3,6,6) = -dl*py/(2d0*csq**(3d0/2d0)) + dl*py*(-3d0*beta - 3d0*pt)*(-beta - pt)/(2d0*c52sq)
te(5,2,2) = -dl*(beta + pt)/(2d0*csq**(3d0/2d0)) - 3d0*dl*px**2d0*(beta + pt)/(2d0*c52sq)
te(1,2,2) = 3d0*dl*px/(2d0*c3sq) + 3d0*dl*px**3d0/(2d0*c52sq)
te(1,2,4) = dl*py/(2d0*c3sq) + 3d0*dl*px**2d0*py/(2d0*c52sq)
te(1,2,6) = dl*(-pt - 1d0/beta)/(2d0*c3sq) + dl*px**2d0*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(1,4,2) = dl*py/(2d0*c3sq) + 3d0*dl*px**2d0*py/(2d0*c52sq)
te(1,4,4) = dl*px/(2d0*c3sq) + 3d0*dl*px*py**2d0/(2d0*c52sq)
te(1,4,6) = dl*px*py*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(1,6,2) = dl*(-pt - 1d0/beta)/(2d0*c3sq) + 3d0*dl*px**2d0*(-pt - 1d0/beta)/(2d0*c52sq)
te(1,6,4) = 3d0*dl*px*py*(-pt - 1d0/beta)/(2d0*c52sq)
te(1,6,6) = -dl*px/(2d0*c3sq) + dl*px*(-3d0*pt - 3d0/beta)*(-pt - 1d0/beta)/(2d0*c52sq)
te(3,2,2) = dl*py/(2d0*c3sq) + 3d0*dl*px**2d0*py/(2d0*c52sq)
te(3,2,4) = dl*px/(2d0*c3sq) + 3d0*dl*px*py**2d0/(2d0*c52sq)
te(3,2,6) = dl*px*py*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(3,4,2) = dl*px/(2d0*c3sq) + 3d0*dl*px*py**2d0/(2d0*c52sq)
te(3,4,4) = 3d0*dl*py/(2d0*c3sq) + 3d0*dl*py**3d0/(2d0*c52sq)
te(3,4,6) = dl*(-pt - 1d0/beta)/(2d0*c3sq) + dl*py**2d0*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(3,6,2) = 3d0*dl*px*py*(-pt - 1d0/beta)/(2d0*c52sq)
te(3,6,4) = dl*(-pt - 1d0/beta)/(2d0*c3sq) + 3d0*dl*py**2d0*(-pt - 1d0/beta)/(2d0*c52sq)
te(3,6,6) = -dl*py/(2d0*c3sq) + dl*py*(-3d0*pt - 3d0/beta)*(-pt - 1d0/beta)/(2d0*c52sq)
te(5,2,2) = -dl*(beta + pt)/(2d0*c3sq) - 3d0*dl*px**2d0*(beta + pt)/(2d0*c52sq)
te(5,2,4) = -3d0*dl*px*py*(beta + pt)/(2d0*c52sq)
te(5,2,6) = -dl*px/(2d0*csq**(3d0/2d0)) - dl*px*(-3d0*beta - 3d0*pt)*(beta + pt)/(2d0*c52sq)
te(5,2,6) = -dl*px/(2d0*c3sq) - dl*px*(beta + pt)*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(5,4,2) = -3d0*dl*px*py*(beta + pt)/(2d0*c52sq)
te(5,4,4) = -dl*(beta + pt)/(2d0*csq**(3d0/2d0)) - 3d0*dl*py**2d0*(beta + pt)/(2d0*c52sq)
te(5,4,6) = -dl*py/(2d0*csq**(3d0/2d0)) - dl*py*(-3d0*beta - 3d0*pt)*(beta + pt)/(2d0*c52sq)
te(5,6,2) = -dl*px/(2d0*csq**(3d0/2d0)) - 3d0*dl*px*(-beta - pt)*(beta + pt)/(2d0*c52sq)
te(5,6,4) = -dl*py/(2d0*csq**(3d0/2d0)) - 3d0*dl*py*(-beta - pt)*(beta + pt)/(2d0*c52sq)
te(5,6,6) = -dl*(-beta - pt)/csq**(3d0/2d0) + dl*(beta + pt)/(2d0*csq**(3d0/2d0)) &
- dl*(-3d0*beta - 3d0*pt)*(-beta - pt)*(beta + pt)/(2d0*c52sq)
te(5,4,4) = -dl*(beta + pt)/(2d0*c3sq) - 3d0*dl*py**2d0*(beta + pt)/(2d0*c52sq)
te(5,4,6) = -dl*py/(2d0*c3sq) - dl*py*(beta + pt)*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(5,6,2) = -dl*px/(2d0*c3sq) - 3d0*dl*px*(beta + pt)*(-pt - 1d0/beta)/(2d0*c52sq)
te(5,6,4) = -dl*py/(2d0*c3sq) - 3d0*dl*py*(beta + pt)*(-pt - 1d0/beta)/(2d0*c52sq)
te(5,6,6) = dl*(beta + pt)/(2d0*c3sq) - dl*(-pt - 1d0/beta)/c3sq - &
dl*(beta + pt)*(-3d0*pt - 3d0/beta)*(-pt - 1d0/beta)/(2d0*c52sq)
endif

orbit(1) = orbit(1) + px*l_pz
orbit(3) = orbit(3) + py*l_pz
orbit(5) = orbit(5) + (dl*beta - (beta + pt) * l_pz)
orbit(5) = orbit(5) + (dl/beta - (1d0/beta + pt) * l_pz)
else

re(1,2) = dl
Expand Down
52 changes: 26 additions & 26 deletions tests/test-twiss-exact/madx_exact.tfs.ref
View file
Open in desktop
Expand Up @@ -4,9 +4,9 @@
@ PARTICLE %06s "PROTON"
@ MASS %le 0.93827208816
@ CHARGE %le 1.00000000000
@ ENERGY %le 2.00000000000
@ PC %le 1.76625181913
@ GAMMA %le 2.13157784958
@ ENERGY %le 1.00000000000
@ PC %le 0.34589808988
@ GAMMA %le 1.06578892479
@ KBUNCH %le 1.00000000000
@ BCURRENT %le 0.00000000000
@ SIGE %le 0.00100000000
Expand All @@ -24,16 +24,16 @@
@ Q2 %le 0.21860189884
@ DQ1 %le 0.00000000000
@ DQ2 %le 0.00000000000
@ DXMAX %le 0.00883657376
@ DYMAX %le 0.17673147524
@ DXMAX %le 0.02892764750
@ DYMAX %le 0.57855295009
@ XCOMAX %le 0.01000200560
@ YCOMAX %le 0.20004011206
@ BETXMAX %le 101.04031624715
@ BETYMAX %le 52.06009815221
@ XCORMS %le 0.00638635935
@ YCORMS %le 0.12772718707
@ DXRMS %le 0.00564222194
@ DYRMS %le 0.11284443887
@ DXRMS %le 0.01847053077
@ DYRMS %le 0.36941061531
@ DELTAP %le 0.00000000000
@ SYNCH_1 %le 0.00000000000
@ SYNCH_2 %le 0.00000000000
Expand All @@ -42,24 +42,24 @@
@ SYNCH_5 %le 0.00000000000
@ SYNCH_6 %le 0.00000000000
@ SYNCH_8 %le 0.00000000000
@ DQMIN %le 0.00000158802
@ DQMIN %le 0.00000000000
@ DQMIN_PHASE %le 0.00000004999
@ TITLE %08s "no-title"
@ ORIGIN %16s "5.07.00 Linux 64"
@ DATE %08s "25/08/21"
@ TIME %08s "00.30.01"
* NAME S X Y PT BETX BETY
$ %s %le %le %le %le %le %le
"SEQ$START" 0.00000000000 0.00000000000 0.00000000000 0.00000000000 1.00000000000 2.00000000000
"DRIFT_0" 1.00000000000 0.00100020056 0.02000401121 0.00000000000 2.00040316247 2.50060098152
"M1" 1.00000000000 0.00100020056 0.02000401121 0.00000000000 2.00040316247 2.50060098152
"DRIFT_1" 3.00000000000 0.00300060168 0.06001203362 0.00000000000 10.00362846224 6.50540883370
"M2" 3.00000000000 0.00300060168 0.06001203362 0.00000000000 10.00362846224 6.50540883370
"DRIFT_2" 5.00000000000 0.00500100280 0.10002005603 0.00000000000 26.01007906179 14.51502453805
"M3" 5.00000000000 0.00500100280 0.10002005603 0.00000000000 26.01007906179 14.51502453805
"DRIFT_3" 7.00000000000 0.00700140392 0.14002807844 0.00000000000 50.01975496110 26.52944809458
"M4" 7.00000000000 0.00700140392 0.14002807844 0.00000000000 50.01975496110 26.52944809458
"DRIFT_4" 9.00000000000 0.00900180504 0.18003610086 0.00000000000 82.03265616019 42.54867950329
"M5" 9.00000000000 0.00900180504 0.18003610086 0.00000000000 82.03265616019 42.54867950329
"DRIFT_5" 10.00000000000 0.01000200560 0.20004011206 0.00000000000 101.04031624715 52.06009815221
"SEQ$END" 10.00000000000 0.01000200560 0.20004011206 0.00000000000 101.04031624715 52.06009815221
@ ORIGIN %16s "5.08.00 Linux 64"
@ DATE %08s "02/02/22"
@ TIME %08s "14.40.18"
* NAME S X Y T PT BETX BETY
$ %s %le %le %le %le %le %le %le
"SEQ$START" 0.00000000000 0.00000000000 0.00000000000 0.00000000000 0.00000000000 1.00000000000 2.00000000000
"DRIFT_0" 1.00000000000 0.00100020056 0.02000401121 -0.00057982489 0.00000000000 2.00040316247 2.50060098152
"M1" 1.00000000000 0.00100020056 0.02000401121 -0.00057982489 0.00000000000 2.00040316247 2.50060098152
"DRIFT_1" 3.00000000000 0.00300060168 0.06001203362 -0.00173947466 0.00000000000 10.00362846224 6.50540883370
"M2" 3.00000000000 0.00300060168 0.06001203362 -0.00173947466 0.00000000000 10.00362846224 6.50540883370
"DRIFT_2" 5.00000000000 0.00500100280 0.10002005603 -0.00289912443 0.00000000000 26.01007906179 14.51502453805
"M3" 5.00000000000 0.00500100280 0.10002005603 -0.00289912443 0.00000000000 26.01007906179 14.51502453805
"DRIFT_3" 7.00000000000 0.00700140392 0.14002807844 -0.00405877420 0.00000000000 50.01975496110 26.52944809458
"M4" 7.00000000000 0.00700140392 0.14002807844 -0.00405877420 0.00000000000 50.01975496110 26.52944809458
"DRIFT_4" 9.00000000000 0.00900180504 0.18003610086 -0.00521842397 0.00000000000 82.03265616019 42.54867950329
"M5" 9.00000000000 0.00900180504 0.18003610086 -0.00521842397 0.00000000000 82.03265616019 42.54867950329
"DRIFT_5" 10.00000000000 0.01000200560 0.20004011206 -0.00579824886 0.00000000000 101.04031624715 52.06009815221
"SEQ$END" 10.00000000000 0.01000200560 0.20004011206 -0.00579824886 0.00000000000 101.04031624715 52.06009815221
60 changes: 30 additions & 30 deletions tests/test-twiss-exact/ptc.tfs.ref
View file
Open in desktop
Expand Up @@ -4,9 +4,9 @@
@ PARTICLE %06s "PROTON"
@ MASS %le 0.93827208816
@ CHARGE %le 1.00000000000
@ ENERGY %le 2.00000000000
@ PC %le 1.76625181913
@ GAMMA %le 2.13157784958
@ ENERGY %le 1.00000000000
@ PC %le 0.34589808988
@ GAMMA %le 1.06578892479
@ KBUNCH %le 1.00000000000
@ BCURRENT %le 0.00000000000
@ SIGE %le 0.00100000000
Expand Down Expand Up @@ -37,24 +37,24 @@
@ BETA12MIN %le 0.00000000000
@ BETA12MAX %le 0.00000002002
@ BETA13MIN %le 0.00000000000
@ BETA13MAX %le 0.00002567481
@ BETA13MAX %le 0.00016736176
@ BETA21MIN %le 0.00000000000
@ BETA21MAX %le 0.00000004005
@ BETA22MIN %le 2.00000000000
@ BETA22MAX %le 52.06009815221
@ BETA23MIN %le 0.00000000000
@ BETA23MAX %le 0.01026992554
@ BETA23MAX %le 0.06694470321
@ BETA31MIN %le 0.00000000000
@ BETA31MAX %le 0.00012837407
@ BETA31MAX %le 0.00083680879
@ BETA32MIN %le 0.00000000000
@ BETA32MAX %le 0.02567481386
@ BETA32MAX %le 0.16736175803
@ BETA33MIN %le 5.00000000000
@ BETA33MAX %le 6.59915529106
@ DISP1MIN %le -0.00506703206
@ BETA33MAX %le 1089.23251036158
@ DISP1MIN %le -0.01293683725
@ DISP1MAX %le 0.00000000000
@ DISP2MIN %le 0.00000000000
@ DISP2MAX %le 0.00000000000
@ DISP3MIN %le -0.10134064113
@ DISP3MIN %le -0.25873674500
@ DISP3MAX %le 0.00000000000
@ DISP4MIN %le 0.00000000000
@ DISP4MAX %le 0.00000000000
Expand All @@ -68,7 +68,7 @@
@ PXCORMS %le 0.00100000000
@ YCORMS %le 0.12772718707
@ PYCORMS %le 0.02000000000
@ TCORMS %le 0.00145006893
@ TCORMS %le 0.00370222756
@ PTCORMS %le 0.00000000000
@ XCOMIN %le 0.00000000000
@ XCOMAX %le 0.01000200560
Expand All @@ -78,26 +78,26 @@
@ YCOMAX %le 0.20004011206
@ PYCOMIN %le 0.02000000000
@ PYCOMAX %le 0.02000000000
@ TCOMIN %le -0.00227102748
@ TCOMIN %le -0.00579824886
@ TCOMAX %le -0.00000000000
@ PTCOMIN %le 0.00000000000
@ PTCOMAX %le 0.00000000000
@ TITLE %08s "no-title"
@ ORIGIN %16s "5.07.00 Linux 64"
@ DATE %08s "25/08/21"
@ TIME %08s "00.30.01"
* NAME S X Y PT BETX BETY
$ %s %le %le %le %le %le %le
"SEQ$START" 0.00000000000 0.00000000000 0.00000000000 0.00000000000 1.00000000000 2.00000000000
"DRIFT_0" 1.00000000000 0.00100020056 0.02000401121 0.00000000000 2.00040316247 2.50060098152
"M1" 1.00000000000 0.00100020056 0.02000401121 0.00000000000 2.00040316247 2.50060098152
"DRIFT_1" 3.00000000000 0.00300060168 0.06001203362 0.00000000000 10.00362846224 6.50540883370
"M2" 3.00000000000 0.00300060168 0.06001203362 0.00000000000 10.00362846224 6.50540883370
"DRIFT_2" 5.00000000000 0.00500100280 0.10002005603 0.00000000000 26.01007906179 14.51502453805
"M3" 5.00000000000 0.00500100280 0.10002005603 0.00000000000 26.01007906179 14.51502453805
"DRIFT_3" 7.00000000000 0.00700140392 0.14002807844 0.00000000000 50.01975496110 26.52944809458
"M4" 7.00000000000 0.00700140392 0.14002807844 0.00000000000 50.01975496110 26.52944809458
"DRIFT_4" 9.00000000000 0.00900180504 0.18003610086 0.00000000000 82.03265616019 42.54867950329
"M5" 9.00000000000 0.00900180504 0.18003610086 0.00000000000 82.03265616019 42.54867950329
"DRIFT_5" 10.00000000000 0.01000200560 0.20004011206 0.00000000000 101.04031624715 52.06009815221
"SEQ$END" 10.00000000000 0.01000200560 0.20004011206 0.00000000000 101.04031624715 52.06009815221
@ ORIGIN %16s "5.08.00 Linux 64"
@ DATE %08s "02/02/22"
@ TIME %08s "14.42.25"
* NAME S X Y T PT BETX BETY
$ %s %le %le %le %le %le %le %le
"SEQ$START" 0.00000000000 0.00000000000 0.00000000000 -0.00000000000 0.00000000000 1.00000000000 2.00000000000
"DRIFT_0" 1.00000000000 0.00100020056 0.02000401121 -0.00057982489 0.00000000000 2.00040316247 2.50060098152
"M1" 1.00000000000 0.00100020056 0.02000401121 -0.00057982489 0.00000000000 2.00040316247 2.50060098152
"DRIFT_1" 3.00000000000 0.00300060168 0.06001203362 -0.00173947466 0.00000000000 10.00362846224 6.50540883370
"M2" 3.00000000000 0.00300060168 0.06001203362 -0.00173947466 0.00000000000 10.00362846224 6.50540883370
"DRIFT_2" 5.00000000000 0.00500100280 0.10002005603 -0.00289912443 0.00000000000 26.01007906179 14.51502453805
"M3" 5.00000000000 0.00500100280 0.10002005603 -0.00289912443 0.00000000000 26.01007906179 14.51502453805
"DRIFT_3" 7.00000000000 0.00700140392 0.14002807844 -0.00405877420 0.00000000000 50.01975496110 26.52944809458
"M4" 7.00000000000 0.00700140392 0.14002807844 -0.00405877420 0.00000000000 50.01975496110 26.52944809458
"DRIFT_4" 9.00000000000 0.00900180504 0.18003610086 -0.00521842397 0.00000000000 82.03265616019 42.54867950329
"M5" 9.00000000000 0.00900180504 0.18003610086 -0.00521842397 0.00000000000 82.03265616019 42.54867950329
"DRIFT_5" 10.00000000000 0.01000200560 0.20004011206 -0.00579824886 0.00000000000 101.04031624715 52.06009815221
"SEQ$END" 10.00000000000 0.01000200560 0.20004011206 -0.00579824886 0.00000000000 101.04031624715 52.06009815221
4 changes: 2 additions & 2 deletions tests/test-twiss-exact/test-twiss-exact.madx
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Open in desktop
Expand Up @@ -7,14 +7,14 @@ m4:marker, at=7;
m5:marker, at=9;
endsequence;
set, format="13.11f";
beam,particle=proton,energy=2;
beam,particle=proton,energy=1;
use, sequence=seq;
option, sympl=false;
px0 = 0.001;
py0 = 0.02;
betx0 = 1;
bety0 = 2;
select, flag = twiss, column=name,s,x,y,pt,betx,bety;
select, flag = twiss, column=name,s,x,y,t, pt,betx,bety;

twiss, file="madx.tfs", betx=betx0, bety=bety0, px=px0, py=py0, pt=pt0;
twiss, file="madx_exact.tfs", betx=betx0, bety=bety0, px=px0, py=py0, exact;
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