1. TraceWin Lattice for FNAL Drift-Tube Linac: Status
Valery Kapin
30-Jul-2014
PIP General Meeting

2. V.Kapin, PIP meeting, July-2014
Contents
Start with the lattice file for FNAL DTLs with old PARMILA based on MM~1968 data (not convenient interface –> command codes)
TraceWin code (only exe, commercial) with user-friendly interface
Existing DTL lattice (by Kim?) for TraceWin used by J.P. (~2013); My inspection -> inaccurate interpretations of “DTL_CELL” elements
TraceWin lattice generation: old PARMILA outputs “DTL_cell” lines via post-processing of MM-data & DTL cell parameters generated by PARMILA’s GENLIN subroutine
Beam dynamics simulations with a nominal Q-stengths: 1) mismatched input beam; 2) input beam matched to DTL acceptances
Beam dynamics simulations with “smoothed” cell-by-cell quadrupole strengths: SG stability diagram => DTL1&2 (BNL pattern)+DTL3-5(FNAL pattern) => larger transverse acceptances (>50%)
Needs for accurate “4-rod RFQ” & MEBT lattices => TraceWin lattice with field maps extracted from MWS for sections/cells
V.Kapin, PIP meeting, July-2014

3. Previous 2013 presentation
Beams-doc-4293-v1
Review previous talks:
- D.McGinnis(2011); - H.J.Kim(Jan-2012)
New restart in Oct-2012 by VK
Optics reconstruction for accelerator model
SNS: XAL(Java) online models
PARMILA new vs old versions
A new configuration for on/off-line modeling
Overview FNAL DTL lattices
FNAL & BNL designs – history
New lattice based on MM68 data is well agree with BNL 1990 lattice and all published design specifications
Questions on intertank distances and quad strengths
About on-line modeling DTL’s pre-injector (4-rod RFQ)
V.Kapin, PIP meeting, July-2014

4. V.Kapin, PIP meeting, July-2014
(F)NAL & BNL DTL tank geometries are the same
V.Kapin, PIP meeting, July-2014

5. V.Kapin, PIP meeting, July-2014
BNL DTL tank had NOT been designed by PARMILA
9-DTL 200-MeV 138m Linac: dL =1.3cm (~0.01%); DW = 170keV (~0.1%)
V.Kapin, PIP meeting, July-2014

6. Example of Messymesh data printout (~1968 for BNL DTL) for one cell
MM calculates E/M parameters of linac cell and output TTFs
V.Kapin, PIP meeting, July-2014

7. Drift-tube geometry - restored
VK01 - only Messymesh data
V.Kapin, PIP meeting, July-2014

8. TTFs from MM68 and might be corrected for tracking
Original Messymesh TTFs have be used for design;
PARMILA should use original for design (step1 - GENLIN),
and refined TTFs for tracking (step2; also for TraceWin)
V.Kapin, PIP meeting, July-2014

9. Restore field tilt in DTL1
C. Curtis et al, in report "fermilab-fn-0201“; HEACC-7, Yerevan, 1969, USSR, p
The plot (left) has been digitized and normalized values from the 1969-plots had been
converted into absolute values of the electrical field strength needed for PARMILA.
The right plot shows the measured field (red circles), the design field (blue-line),
the gap fields set with by PARMILA's command "CHANGE=4" (green crosses).
V.Kapin, PIP meeting, July-2014

10. V.Kapin, PIP meeting, July-2014
Start with the lattice file for FNAL DTLs based on Messymesh~1968 data with old PARMILA
V.Kapin, Post-processing for old Parmila (SY12): notes with examples for FNAL DTL, June-2013, 20pages
OUTPROC:
SUBNUM# command codes:
not convenient interface
NOT for a CASUAL (MODERN) USER!
The example plot from data in <OUT1_good_bad_particles.out>
for FNAL DTL1-5 (text-file => external plotting soft):
V.Kapin, PIP meeting, July-2014

11. Old PARMILA: SUBNUM8 example
: SUBNUM 8 : Plots two profiles as functions of cell number
SUBNUM 8
: (34) dPhi & dW profiles: dPhiMax=180deg dWmax=1MeV
OUTPUT
OPTCON 0 0
Coding
Number for plot
Types and frame
sizes
V.Kapin, PIP meeting, July-2014

12. V.Kapin, PIP meeting, July-2014
TraceWin code (only EXEcutable, commercial) with a user-friendly interface
What physics is inside?
“DTL_CELL” ?
Source code is not available;
Manual is in a laconic & briefly style (in English, but some chapters in French)
Need to communicate
With code owners !
In red box:
from my
communications
V.Kapin, PIP meeting, July-2014

13. TraceWin code (con-ed)
What physics is inside?
“DTL_CELL” ?
V=E0*T*L, Qs –
Must be known “a priory” –
They are written into a lattice file !
Supposing
A true design particle!
V.Kapin, PIP meeting, July-2014

14. V.Kapin, PIP meeting, July-2014
“Wangler’s book page 202”
What physics is inside?
“DTL_CELL” ?
Tracking according to Lapostolle & Co treatment, not PARMILA’s (Swenson’s style) – see discussion in LINAC bible (1970)
In multi-step integration (e.g.Runge-Kutta – time&memory consuming!)
TTF definitions are different from PARMILA’s !
TTFs are expanded around a given synchronous particle => still “design code” !
Exact implementation in TraceWin is unknown … (e.g. at center or entrance)
V.Kapin, PIP meeting, July-2014

15. Discussion from LINAC bible 1970
Tracking method in TraceWin
according to Lapostolle’s
Formulae is similar to one in
PARMILA’s (Swenson’s style):
“Drift+thin-lens+drift”
V.Kapin, PIP meeting, July-2014

16. Existing TraceWin Start-to-end lattice
J.P. Carneiro, The FNAL 400 MeV Linac in TRACEWIN (from Ion Source to Stripping Foil), PIP meeting, 12-June-2013.
Start-to-end Model with TRACEWIN; (TRACEWIN and TOUTATIS;)
Citation: “How was the model built ?
LEBT (35 keV): from TRACE2D input file (CY Tan, D. Bollinger)
RFQ (750 keV) : from PARMTEQM input file (CY Tan)
MEBT +DTL (117 MeV) + CCL (400 MeV) : from PARMILA input file (H.J. Kim)”
Out: TraceWin lattice file “fnal_pip_linac.dat” containing
“RFQ_CELL”, “DTL_CELL” (by Kim ?) etc. commands
V.Kapin, PIP meeting, July-2014

17. Inspection of existing TraceWin lattice
inaccurate interpretations of “DTL_CELL” elements
Gap shift ignored:
As for symmetrical cell
R aperture 20mm assumed
everywhere in DTL1-5
Wrong by factor “-2p”
Inaccurate values will affect on beam dynamics results:
Equivalent particle trajectory – position of trajectory bend due to the gap center position (“drift+kick+drift”);
Particle losses – largest & constant radius of aperture (instead of stepwise increase 1.0;1.25;1.5;2.0)
Equivalent particle trajectory – shift value for both phase & radial position due to wrong value of T’(k)
V.Kapin, PIP meeting, July-2014

18. TraceWin lattice generation
Old PARMILA (with specially written using FORTRAN source code) outputs
“DTL_cell” lines via post-processing of MessyMesh-data &
DTL cell parameters generated by PARMILA’s GENLIN subroutine
Several parameters are needed at the cell centers
(not at the ends as in PARMILA)
Methods for particle tracking through the gaps in PARMILA & TraceWin are different, but based on the same approach (“drift+kick+drift”).
Benchmarking of results might be useful.
V.Kapin, PIP meeting, July-2014

19. V.Kapin, PIP meeting, July-2014
Beam dynamics with a nominal Q-strengths; Finding Longitudinal Acceptance DTL1-5
Within separatrix –
non-linear oscillations
Beam: exy-> 0;
Ibeam=0
Zoom
Surv. Particles
At DTL1 Entry
V.Kapin, PIP meeting, July-2014

20. Finding Long. Acceptance DTL1-5(con-ed)
Particles with non-linear oscillations
Surv. Particles
At DTL5 Exit
Surv. Particles
At DTL1 Entry
TraceWin provides approx. ellipse
Parameters & its shift:
V.Kapin, PIP meeting, July-2014

21. Long. Accept.: small (linear) oscillations
1) drawing inscribed "small (linear oscillations)" 25%-ellipse
with a plotting soft (a&b=const; shifted center)
2) superpose it on large accept.
Test run with 0%-loss (Beam: exy-> 0; Ibeam=0):
Figs: Entry; Exit; e(z)
V.Kapin, PIP meeting, July-2014

22. V.Kapin, PIP meeting, July-2014
Beam dynamics with a nominal Q-stengths; Finding Transverse Acceptance X-X’plane
Particles At DTL1 Entry – (survived=dark):
Inj. beam:
ey,L-> 0;
Ibeam=0
Zoom
Zoom
Entry & Exit
Not yet 100%
V.Kapin, PIP meeting, July-2014

23. V.Kapin, PIP meeting, July-2014
Beam dynamics with a nominal Q-stengths; Finding Trans. X-X’ Accept. (con-ed)
Reduce x-emittance until 100% transm. is reached
DTL1
Entry:
DTL5
Exit:
V.Kapin, PIP meeting, July-2014

24. V.Kapin, PIP meeting, July-2014
Beam dynamics with a nominal Q-stengths; Finding Transverse Acceptance: Y-Y’plane
Reduce y-emittance until 100% transm. is reached (as for x-x’)
DTL1
Entry:
DTL5
Exit:
V.Kapin, PIP meeting, July-2014

25. Partial acceptances & unmatched input beam
Calculated partial acceptances (for 0%-loss, I=0 & zero emittances in other planes)
Initial parameters of unmatched injected beam (file "pmi2tw.dst" by new PARMILA): Input
V.Kapin, PIP meeting, July-2014

26. V.Kapin, PIP meeting, July-2014
Unmatched input beam
Blue ellipses
acceptances;
red elipses:
Total 5-rms
Emittances
(unnorm.)
Iout(Iinp=2mA)=1.76mA (88%)
Iout(Iinp=50mA)=43.2mA (86%)
Iout(Iinp=100mA)=68mA (68%)
Imax(Iinp=140mA)=74mA (53%)
Current dependent e-growth
In all 3 phase space
(L~2; X~4; Y~6.5 times)!
V.Kapin, PIP meeting, July-2014

27. V.Kapin, PIP meeting, July-2014
Matched input beam
Blue ellipses - DTLs acceptances; red elipses: Total 5-rms beam Emittances (unnorm.)
V.Kapin, PIP meeting, July-2014

28. Matched input beam: e-growth & I-transmission
Current dependent e-growth
In all 3 phase space
(L~2; X~6; Y~6.5 times)!
V.Kapin, PIP meeting, July-2014

29. Losses %: matched vs mismatched (Iinj=1mA& 45mA)
V.Kapin, PIP meeting, July-2014

30. Ibeam mA: matched vs mismatched (Iinj=1mA & 45mA)
V.Kapin, PIP meeting, July-2014

31. ez,norm: matched vs mism. (Iinj=1mA & 45mA)
V.Kapin, PIP meeting, July-2014

32. e t,norm: matched vs mism. at Iinj=1mA & 45mA:
V.Kapin, PIP meeting, July-2014

33. On emittance growth in proton linacs
References:
1972 Batchelor Emittance vs Quads BNL LINAC_p47;
1979 Jameson & Mills EmittanceGrowth in Linacs LinacConfProcs_p231
1979 Jameson Emittance Growth in Linacs HeavyIonFusionWorkshop_p84
1985 Wangler Emittance Growth of IntenseBEam PAC1985_2196
2008 Reiser Emittance Growth Ch06 in his book
2008 Wangler SpCh Multiparticle Dynamic ch09 in RF linacs book
2010 Wei Simulations of Errors JPARC Linac
V.Kapin, PIP meeting, July-2014

34. Quad. Strengths and Smith-Gluckstern stability diagram
BNL linac (1990)
FNAL linac (nomin. Qs)
Quads in DTL1
V.Kapin, PIP meeting, July-2014

35. Simple Smoothing of quad. G(nq)
Quad. gradient G vs quad number nq :
for DTL1&2 use BNL’s (AK90); for DTL3-5 use FNAL’s nominal (FG01).
Liner interpolation; equate adjacent Quad pairs (common power supply)
Keep Quad-settings at the tank ends (matching between tanks in a future)
V.Kapin, PIP meeting, July-2014

36. V.Kapin, PIP meeting, July-2014
Q-smoothing DTL3-5
V.Kapin, PIP meeting, July-2014

37. Increased acceptances for smoothed G(nq)
a) blue= original; red = smoothed Quads
X-acceptance:
1.5->2.3
Y-acceptance:
1.4->4.0
Y-Y’ plane
X-X’ plane
b) blue= original; red = smoothed (Q2-3 exactly as AK90)
X-acceptance:
1.5->2.6
Y-acceptance:
1.4->2.6
(w/o matching
With MEBT beam
at DTL1 entry)
V.Kapin, PIP meeting, July-2014

38. Known & unknown DTL parameters
XY e; centroid;
I, A
4-rod
RFQ
MEBT
RF cavity
& Quads
~Long e
(PARMTEQ, tests)
W-Phi Centroid
DTL1:
E+d, PhiS+d,
56 gaps;
57 Quads
Grad(Qi, Qi+1)=
F(I)+d
DTL2:
E+d,
PhiS+d,
60 gaps;
61Quads
DTL3:
35 gaps;
36 Qs
BPMs ;
DTL4:
29 gaps;
30 Qs
DTL5:
24 gaps;
25 Qs
RF param.: Power Prf & phases between resonators dPhi are tuned for best Ibeam !?
Prf & dPhi values unknown; different from design values E0 & PhiS used by TraceWin !
This difference affects on both long. & transv. Tracking results!
Actual E0 & PhiS must be recalculated (additional code or another code, e.g. TRACK?
Quad param.: Gradients are calculated from currents with ideal formulae ~5-10%
There is no dipoles & BPMs inside => usual optics reconstruction is impossible
Intertank BPMs: for correction of coherent oscillations (ini. Beam or misalignments)
Initial beam: Transv. Emittances are measured (at what conditions ?);
Long. Emittance – upright ellipse (ideal MEBT) via PARMTEQ (not for 4-rod RFQ)
Particle Distributions (Gaussian etc) are unknown !
V.Kapin, PIP meeting, July-2014

39. Existing 4-rod RFQ lattice with TraceWin
RFQ (750 keV) : from PARMTEQM input file (CY Tan)
RFQ: RFQ_CELL; RFQ_GAP_RMS_FFS etc.
TraceWin manual:
Analytical function for ideal RFQ with pure quad-symmetry (like 4-vane RFQ):
Type: 2=>Acc. cell; 3=> Front end cell; 4=>Transcell
V.Kapin, PIP meeting, July-2014

40. Need for a correct TraceWin lattice for 4-rod RFQ
Existing TraceWin lattice (based on PARMTEQ-M lattice)
It ignore its inherent asymmetry; it describes an ideal RFQ with ideal Quad-symmetry like 4-vane RFQ (w/o dipoles)
Problems are in matching section and regular RFQ channel, where additional components generated.
Experimentally 4-rod RFQ never had a high transmission as PARMTEQ(M) predicted
Existing TraceWin lattice will not model features of 4-rod RFQ (acceptance; emittance & shifts of beam centroid).
I had worked on 4-rod RFQ simulations in 198x-199x (EPAC-94, Linac-94, JJAP-97) (see APCsem-2013)
Additional non-quadrupole fields in 4-rod RFQ were shown and a new model for beam dynamics simulations was used
I guess now it is possible simulate 4-rod RFQ with TraceWin using field maps from MWS
V.Kapin, PIP meeting, July-2014

41. V.Kapin, PIP meeting, July-2014
Conclusion
TraceWin lattice for FNAL DTL1-5 is updated
Long. & Transv acceptances are calculated
Beam transmission and emittance growth for matched and unmatched beam are compared
Beam transmission for matched beam ~97% at 50mA
Emittance growth depends on Ibeam (unavoidable); it is the same for matched and unmatched beams
Simple smoothing of Grad(nq) increases accept. (>50%); Matching at entry and in inter-tanks might be needed
Limitations for simulations of a real beam discussed; supplementary or other code (a’la TRACK) is needed
The lattices for MEBT & 4-rod RFQ should be studied & updated for more accurate simulations
V.Kapin, PIP meeting, July-2014