TRACK vs Partran Benchmarking Version 2 (It is better to be - PowerPoint PPT Presentation

TRACK vs Partran Benchmarking Version 2 (It is better to be approximately right than exactly wrong !) J.F Ostiguy/ APC ostiguy@fnal.gov Ostiguy - Track vs Partran Benchmarking Version 2

Issues ● A while ago, we performed some comparisons of beam envelopes predicted by TRACK and Partran. The agreement was deemed satisfactory. ● Recently, it has been reported by (A. Saini) that the envelopes predicted by TRACK and Partran do not seem to agree very well for recent versions of the CW linac (650 MHz cavities only) Is this due to differences in rf fields, in SC kicks computations, initial distributions ? ● Since (for now) we are mostly relying on TRACK for statistical error analysis, and TraceWin/Partran for design, we need to be confident that (1) the codes are correct and (2) the lattice models in both codes are equivalent. Ostiguy - Track vs Partran Benchmarking Version 2

Lattice Files ● For efficiency and to minimize the potential for translation errors, a program was written and is used to automatically translate a Tracewin/Partran lattice into a TRACK lattice ● Note: TraceWin uses hard-edge quads. For this reason, the translated TRACK lattice does the same; TRACK default is to include fringe fields based on Enge functions with sensible coefficients. Ostiguy - Track vs Partran Benchmarking Version 2

Field Maps ● TraceWin/PARTRAN can use either transverse field expansions based on a 1D axial map or full 3D maps interpolated on a rectangular or cylindrical grid. ● TRACK can only use full 3D field maps interpolated on a rectangular grid (confirmed with B. Mustapha at Argonne) ● TRACK grid resolution is fixed: 24 x 24 x 200 cells. ● PARTRAN grid resolution is variable. Ostiguy - Track vs Partran Benchmarking Version 2

Axial Expansions vs Full 3D Maps ● The current PX linac front-end is essentially optically axi-symmetric ( solenoidal focusing). True, there is some small local asymmetry in the spoke cavities. That said, near the axis, within the 3σ beam (< 4 mm), this asymmetry is expected to be negligible. ● By construction, axial expansions produce fields that locally satisfy M.E. exactly, everywhere. ● Interpolation on a grid does not produce fields that locally satisfy M.E exactly (this is not necessarily an issue for a single pass machine ). On the other hand, when the fields are truly axi-symmetric, it is important to interpolate in a way that does not violate this symmetry. This require a symmetric grid. ● Conversely, if the fields are truly not axisymmetric, an axial expansion obviously cannot represent this. Ostiguy - Track vs Partran Benchmarking Version 2

About Field Map and Phase Reference Conventions TRACK defines the cavity phases w/r to the “synchronous” phase i.e. the ● phase that corresponds to max energy gain. There is no other available option. TraceWin/Partran defines the rf phases w/r to the reference rf phases at ● the entrance of the cavity field maps. A cos(wt+φ) dependence is assumed for the E field and a -sin(wt+φ) dependence is assumed for the B field. Optionally, the synchronous phase convention may also be used using the explicit SET_SYNC_PHASE command. An interesting side effect of this is that in TRACK, the results are never ● affected by sign factor in the map field amplitudes i.e. -k scaling produces the same results as a k scaling. In PARTRAN/TraceWin, unless SET_SYNC_PHASE is used explicitly, the ● sign of the field map matters i.e changing the field scale factor from k to -k will (obviously) result in deceleration. Ostiguy - Track vs Partran Benchmarking Version 2

Procedure ● So far, all work done with TraceWin Partran has been done using maps based on axial expansions ● For comparisons purposes, all the TRACK field maps were translated to PARTRAN format without changing anything to the mesh size or to the interpolated values. ● Assume I=0 to distinguish rf effects from SC effects ● The synchronous phase convention was used consistently with both programs. Ostiguy - Track vs Partran Benchmarking Version 2

TRACK vs PARTRAN (Axial expansions) Ostiguy - Track vs Partran Benchmarking Version 2

TRACK vs PARTRAN (Axial expansions) Ostiguy - Track vs Partran Benchmarking Version 2

TRACK vs PARTRAN (3D Fields+entrance phases) No Particle loss – Better agreement between TRACK and PARTRAN Ostiguy - Track vs Partran Benchmarking Version 2

TRACK vs PARTRAN 3D (3D Maps + entrance phases) Ostiguy - Track vs Partran Benchmarking Version 2

Synchronous vs Entrance Phases ● TRACK uses only synchronous phases in the lattice file. The entrance phases are provided as output. ● By default, TraceWin uses the entrance phases as input. Synchronous phases can also be used as input if SET_SYNC_PHASE is invoked. ● For v < 2.3.2.2, the entrance phases were not available if the synchronous phases were used in the lattice file. ● SET_SYNC_PHASE should not be used in conjunction with dynamic phase errors. Ostiguy - Track vs Partran Benchmarking Version 2

Can You Spot the Problem ? Can You Spot the Problem ? (ignore the scale factors) (ignore the scale factors) Example: SSR-1 Cavity Example: SSR-1 Cavity Axial field profile from TraceWin Axial profile extracted from TRACK field built-in field viewer after direct map file. conversion of the TRACK field map. Ostiguy - Track vs Partran Benchmarking Version 2

Earlier Problems with 3D Fields… Explained ! ● TRACK field map local longitudinal coordinate origin is at the center of the map (usually a symmetry point) ● TRACK integration is from -L/2 to L/2, where L is the cavity length ● TRACK Field map extent ≠ cavity length ! ● TraceWin/Partran field map local longitudinal coordinate origin coincides with upstream end of field map ● TraceWin/Partran integration is from 0 to L ● TraceWin/Partran map extent ≠ cavity length ! ● With the same field map, TraceWin/Partran and Track will yield different results unless field map extent = cavity length ● The TRACK convention for local field map coordinates is more logical. It may be supported by TraceWin in a future version. Ostiguy - Track vs Partran Benchmarking Version 2

Recent TraceWin Mod TraceWin was recently modified so that entrance phase is now always available, independently of whether input or synchronous phase has been used in the lattice file. Ostiguy - Track vs Partran Benchmarking Version 2

Partran 3D Fields vs TRACK 3D Fields (SC on, I = 10 mA) Note : Only low energy part displayed (~1/2 of linac) Ostiguy - Track vs Partran Benchmarking Version 2

Partran 3D Fields vs Track 3D Fields (SC on , I =10 mA) Note : Only low energy part displayed (~1/2 of linac) Ostiguy - Track vs Partran Benchmarking Version 2

A Note About the SC Mesh in TRACK ● In TRACK, the default SC mesh extends all the way to the aperture limit transversely and over a full rf period at the current frequency longitudinally. ● It turns out that these settings can be overridden, as follows: 1 prmtr xylhSC=10. 1 prmtr zlhSC=5. In this example, the first command sets the transverse mesh size to 10 x the geometric mean of the x,y sizes and the second one sets the longitudinal mesh size to 5 x the rms bunch length. Ostiguy - Track vs Partran Benchmarking Version 2

Conclusions ● With 3D fields maps, agreement between TRACK and TraceWin/Partran is excellent. ● Care is needed to generate the 3D field maps correctly, given the different conventions. ● There are small, but nevertheless sometimes noticeable, differences between envelopes predicted with 3D field maps vs those predicted using axial expansions. ● Final calculations (esp. large scale statistical error runs) should be checked with full 3D maps. Ostiguy - Track vs Partran Benchmarking Version 2