be beams department€¦ · be beams department ch!2 plan 1. overview: survey, track, cofind,...

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BE Beams Department

Laurent DeniauCERN-BE/ABP

5th December 2018

Methodical Accelerator Design - Next GenerationSurvey and Plot commands (2/5)ABP-HSS meeting

BE Beams Department

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!2

PLAN

1. Overview: Survey, Track, Cofind, Twiss, Match, Plot Unification and (re)use of the command interfaces.

2. Survey command and Plot command. Geometrical tracking.

3. Track command and Beam command. Dynamical tracking.

4. Twiss command and Cofind command. Tracking DA maps, computing optical functions.

5. Match command. Optimising lattices, functions optima.

Annexes I. Object model, Commands, Environments.

II. MTable, Sequence, Elements.

III. Symplectic integrators. IV. DA maps, GTPSA.

V. Linear Algebra.

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!2

PLAN









V. Linear Algebra.









V. Linear Algebra.

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Geometrical tracking

!3

MAD-NGCore

Linear ToolBoxReal & ComplexVector & Matrix

AlgorithmsSolvers, Eigen,FFT, Optimisers

DA ToolboxReal & Complex

GTPSA

MADX Env

Elements

Sequence

Beam

ObjectModel

MTablePlot

Commands

Survey

Track

COFind

Twiss

Match

DA Map

Geometric3D Maps

SymplecticIntegrators

Unit Tests

Dynamic6D Maps

2018

Emit

2019

IBS

2019?

COCorrect

2019

Spin Maps

2020?Radiation

2019

A uses BA B

A exposes BA B

A is-a BA B

Geo/LinAlg Dyn/DiffAlgLegend

TodoDone Dev

Normal form Optical Funs

2019

Aperture

2019

Unification

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Survey examples (MADX vs MAD)

!4

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! global workspace, no ‘import’

-- classesdip: sbend,l=10,angle=2*pi/12,tilt=0.1;midseq: marker;-- sequencemusr: sequence, refer=centre, l=120; dip1 : dip, at=5; dip2 : dip, at=5+10; dip3 : dip, at=5+20; dip4 : dip, at=5+30; dip5 : dip, at=5+40; dip6 : dip, at=5+50; midseq, at=60; dip7 : dip, at=5+60; dip8 : dip, at=5+70; dip9 : dip, at=5+80; dip10: dip, at=5+90; dip11: dip, at=5+100; dip12: dip, at=5+110;endsequence;-- commandbeam,particle=proton;use,period=musr;select,flag=survey,clear;select,flag=survey,column=name,keyword, l,angle,x,y,z,theta,phi,psi;survey,file=“test-survey_1.tfs”;

Simple MADX survey example


!4

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local beam, sequence, survey in MADlocal sbend, marker in MAD.elementlocal pi in math-- classeslocal dip= sbend {l=10,angle=2*pi/12,tilt=0.1}local mk = marker-- sequencelocal musr = sequence 'musr' {refer='centre',l=120, dip 'dip1' {at=5 }, dip 'dip2' {at=5+10 }, dip 'dip3' {at=5+20 }, dip 'dip4' {at=5+30 }, dip 'dip5' {at=5+40 }, dip 'dip6' {at=5+50 }, mk 'midseq'{at=60 }, dip 'dip7 ' {at=5+60 }, dip 'dip8 ' {at=5+70 }, dip 'dip9 ' {at=5+80 }, dip 'dip10' {at=5+90 }, dip 'dip11' {at=5+100}, dip 'dip12' {at=5+110},}-- command! no beam required

local col= {'name','kind','l','angle', 'x','y','z','theta','phi','psi'}local tbl= survey {sequence=musr}tbl:write(“test-survey_1.tfs”, col)

Simple MAD survey example

! global workspace, no ‘import’

-- classesdip: sbend,l=10,angle=2*pi/12,tilt=0.1;midseq: marker;-- sequencemusr: sequence, refer=centre, l=120; dip1 : dip, at=5; dip2 : dip, at=5+10; dip3 : dip, at=5+20; dip4 : dip, at=5+30; dip5 : dip, at=5+40; dip6 : dip, at=5+50; midseq, at=60; dip7 : dip, at=5+60; dip8 : dip, at=5+70; dip9 : dip, at=5+80; dip10: dip, at=5+90; dip11: dip, at=5+100; dip12: dip, at=5+110;endsequence;-- commandbeam,particle=proton;use,period=musr;select,flag=survey,clear;select,flag=survey,column=name,keyword, l,angle,x,y,z,theta,phi,psi;survey,file=“test-survey_1.tfs”;



!4

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Survey tables (MADX vs MAD)

!5

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@ NAME %06s "SURVEY"@ TYPE %06s "SURVEY"@ TITLE %08s "no-title"@ ORIGIN %17s "5.04.02 Darwin 64"@ DATE %08s "04/12/18"@ TIME %08s "23.38.49"* NAME KEYWORD L ANGLE X Y Z THETA PHI PSI$ %s %s %le %le %le %le %le %le %le %le "MUSR$START" "MARKER" 0 0 0 0 0 0 0 0 "DIP1" "SBEND" 10 0.5235987756 -2.545943335 -0.2554463896 9.549296586 -0.5214328139 -0.04993746099 -0.01332532711 "DIP2" "SBEND" 10 0.5235987756 -9.501589878 -0.9533389047 16.53986686 -1.045026159 -0.08656635199 -0.04987468693 "DIP3" "SBEND" 10 0.5235987756 -19.00317976 -1.906677809 19.09859317 -1.570796327 -0.1 -0.1 "DIP4" "SBEND" 10 0.5235987756 -28.50476963 -2.860016714 16.53986686 -2.096566495 -0.08656635199 -0.1501253131 "DIP5" "SBEND" 10 0.5235987756 -35.46041618 -3.557909229 9.549296586 -2.62015984 -0.04993746099 -0.1866746729 "DIP6" "SBEND" 10 0.5235987756 -38.00635951 -3.813355619 -3.93995947e-12 -3.141592654 2.063627047e-14 -0.2 "MIDSEQ" "MARKER" 0 0 -38.00635951 -3.813355619 -3.93995947e-12 -3.141592654 2.063627047e-14 -0.2 "DIP7" "SBEND" 10 0.5235987756 -35.46041618 -3.557909229 -9.549296586 -3.663025467 0.04993746099 -0.1866746729 "DIP8" "SBEND" 10 0.5235987756 -28.50476963 -2.860016714 -16.53986686 -4.186618812 0.08656635199 -0.1501253131 "DIP9" "SBEND" 10 0.5235987756 -19.00317976 -1.906677809 -19.09859317 -4.71238898 0.1 -0.1 "DIP10" "SBEND" 10 0.5235987756 -9.501589878 -0.9533389047 -16.53986686 -5.238159148 0.08656635199 -0.04987468693 "DIP11" "SBEND" 10 0.5235987756 -2.545943335 -0.2554463896 -9.549296586 -5.761752493 0.04993746099 -0.01332532711 "DIP12" "SBEND" 10 0.5235987756 -2.842170943e-14 -1.498801083e-15 7.897682508e-12 -6.283185307 -4.13141743e-14 1.734723476e-17 "MUSR$END" "MARKER" 0 0 -2.842170943e-14 -1.498801083e-15 7.897682508e-12 -6.283185307 -4.13141743e-14 1.734723476e-17



!5

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@ title %04s "musr"@ type %06s "survey"@ origin %16s "MAD 0.5.4 OSX 64"@ date %08s "04/12/18"@ time %08s "23:39:23"@ refcol %04s "name"@ direction %le 1@ observe %le 0@ implicit %b false@ relative %b false* name kind l angle x y z theta phi psi$ %s %s %le %le %le %le %le %le %le %le "$start" "marker" 0 0 0 0 0 0 0 0 "dip1" "sbend" 10 0.5235987756 -2.545943335 -0.2554463896 9.549296586 -0.5214328139 -0.04993746099 -0.01332532711 "dip2" "sbend" 10 0.5235987756 -9.501589878 -0.9533389047 16.53986686 -1.045026159 -0.08656635199 -0.04987468693 "dip3" "sbend" 10 0.5235987756 -19.00317976 -1.906677809 19.09859317 -1.570796327 -0.1 -0.1 "dip4" "sbend" 10 0.5235987756 -28.50476963 -2.860016714 16.53986686 -2.096566495 -0.08656635199 -0.1501253131 "dip5" "sbend" 10 0.5235987756 -35.46041618 -3.557909229 9.549296586 -2.62015984 -0.04993746099 -0.1866746729 "dip6" "sbend" 10 0.5235987756 -38.00635951 -3.813355619 1.421085472e-14 -3.141592654 -2.081668171e-17 -0.2 "midseq" "marker" 0 0 -38.00635951 -3.813355619 1.421085472e-14 -3.141592654 -2.081668171e-17 -0.2 "dip7 " "sbend" 10 0.5235987756 -35.46041618 -3.557909229 -9.549296586 -3.663025467 0.04993746099 -0.1866746729 "dip8 " "sbend" 10 0.5235987756 -28.50476963 -2.860016714 -16.53986686 -4.186618812 0.08656635199 -0.1501253131 "dip9 " "sbend" 10 0.5235987756 -19.00317976 -1.906677809 -19.09859317 -4.71238898 0.1 -0.1 "dip10" "sbend" 10 0.5235987756 -9.501589878 -0.9533389047 -16.53986686 -5.238159148 0.08656635199 -0.04987468693 "dip11" "sbend" 10 0.5235987756 -2.545943335 -0.2554463896 -9.549296586 -5.761752493 0.04993746099 -0.01332532711 "dip12" "sbend" 10 0.5235987756 -6.217248938e-15 -1.665334537e-16 -2.131628207e-14 -6.283185307 6.938893904e-17 9.714451465e-17 "$end" "marker" 0 0 -6.217248938e-15 -1.665334537e-16 -2.131628207e-14 -6.283185307 6.938893904e-17 9.714451465e-17





!5

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!5

TFS tables

saved in files

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!5

Column used as dictionary for direct table row access e.g. print(tbl.dip7.theta) displays -3.663025467

TFS tables

saved in files

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Survey interface

!6

survey = command 'survey' { beam=_na, -- N/A sequence=nil, -- sequence (required) range=nil, -- range of tracking dir=1, -- s-direction of tracking (1 or -1)

s0=0, -- initial s X0={0,0,0}, -- initial coordinates x, y, z A0={0,0,0}, -- initial angles theta, phi, psi W0=nil, -- initial W matrix (companion of X0)

mapdef=_na, -- always use matrix formalism (i.e. true) mapsave=false, -- save the orientation matrix W (rotations)

nturn=1, -- number of turns nstep=-1, -- number of elements to track nslice=1, -- number of slice for each element implicit=false, -- slice implicit elements too misalign=0, -- 0 none, 1 main, 2 main+error

save=true, -- create mtable and save results title=nil, -- title of mtable (default seq.name) savesel=fnone, -- save selector relative=false, -- save length of slices instead from element start observe=false, -- save only in observed elements (every n turns)

atentry=fnone, -- action called when entering an element atslice=fnone, -- action called after each element slices atexit=fnone, -- action called when exiting an element ataper=_na, -- N/A atsave=fnone, -- action called after saving in mtable

usrdef=nil, -- user defined data attached to the mflow mflow=nil, -- mflow, exclusive with other attributes except nstep exec=exec, -- command to execute upon children creation} :set_readonly() -- reference survey command is readonly

MAD-X like input & setup

Initial setup

Maps setup

Track setup

Save setup

Actions setup: user customisation

User data

Map flow: ongoing survey command

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Element tracking (Survey, Track, Cofind and Twiss)

!7

๏ Thick elements can contain thin sub-elements and patches. ๏ Sub-elements are “at” relative positions, at = pos with 0 ≤ pos ≤ 1. ๏ Tracking to sub-elements (Mthick) takes slicing (nslice) into account. ๏ Tracking directions and (internal) variables:

➡ element direction: edir ➠ affects curvatures (edir = seq.dir). ➡ tracking direction (s): sdir ➠ affects lengths (sdir = cmd.dir). ➡ time direction (t): tdir ➠ affects angles ( tdir = edir x sdir). ➡ beam direction: bdir ➠ affects strengths (bdir = edir x sdir x chg).

Reverse tracking

Back tracking

Signed tracking

thin

thin

thin

P-1P

thin

thin

thick [ ]

~P

~P-1

Mthick Mthick Mthick Mthick

Mdrift

M-1thick M-1thick M-1thick M-1thick

[1] [2] [3] [4] [5]

s > s0Forward

s < s0Backward

M-1drift

Mdrift

M-1drift

extern

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Element slicing (Survey, Track, Cofind and Twiss)

!8

P-1P thick { }

Mthick

extern

{0} {1} {2} {3} {4}{-1} {-2}

atslice atslice atslice atslice atsliceMthick Mthick Mthick

atentry atexit

M-1thick M-1thick M-1thick M-1thick{4} {3} {2} {1} {0}

Mdrift

M-1drift

Mdrift

M-1drift

ataper atsave

ataperatsave

atexit atentry

s > s0Forward

s < s0Backward

{-2} {-1}

๏ Uniform slicing: nslice = N ➠ Lslice_i = Lelem/N.

๏ Non-uniform slicing: nslice = {lw1, lw2, …, lwk} with ∑ lwi = 1 and N = #nslice ➠ Lslice_i = Lelem x lwi.

๏ Slices selectors: ➡ atbegin ➠ active at {0} ➡ atbody ➠ active at {1..N} ➡ atins ➠ active at {1..N-1} ➡ atmid ➠ active at {N/2} (not active for even N) ➡ atend ➠ active at {N} ➡ atbound ➠ active at {0,N}

MADX survey

cannot slice

(wrong with tilt <> 0)

Useful to see misalignments

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Plot example (single curved layout & many features)

!9

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Plot example (single curved layout & many features)

!9

local plot1 = plot { sequence = lhcb1, range = { 'E.DS.L5.B1', 'S.DS.R5.B1' }, table = mtbl, tablerange = { 100, 400 }, x1y1 = { x = { 'y', 'z' } }, yrange = { -1.2, 1.2 }, colors = { y = 'red', z = 'green' }, styles = { y = "lines", z = "linespoints" }, dashtypes = { y = ".. ", z = "-- " }, pointtypes = { z = 4 }, legendfont = "Times New Roman", legendsize = 21, legendpos = "top right", legend = {y = "{/Symbol b} + \u{03b2}", z = "{/Symbol B} + \u{0392}"}, xlabel = "Absciss label", ylabel = "Ordinate label",}

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Plot example (single straight layout & multiplot in PDF)

!10

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!10

-1-0.50

0.51

0 100 200 300 400 500

Ordinatelabel

Absciss label

plot MAD 0.5.4, 05/12/18, 00:12:10

β + βΒ + Β

-1-0.50

0.51

0 100 200 300 400 500

Ordinatelabel

Absciss label

plot MAD 0.5.4, 05/12/18, 00:12:10

y

-1-0.50

0.51

0 100 200 300 400 500

Ordinatelabel

Absciss label

plot MAD 0.5.4, 05/12/18, 00:12:10

y

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!10

-1-0.50

0.51

0 100 200 300 400 500

Ordinatelabel

Absciss label

plot MAD 0.5.4, 05/12/18, 00:12:10

β + βΒ + Β

-1-0.50

0.51

0 100 200 300 400 500

Ordinatelabel

Absciss label

plot MAD 0.5.4, 05/12/18, 00:12:10

y

-1-0.50

0.51

0 100 200 300 400 500

Ordinatelabel

Absciss label

plot MAD 0.5.4, 05/12/18, 00:12:10

y

lhcb1:set_layangle(false)local multi1 = plot1 { sid = newid(), prolog = "set multiplot", output = "plot-multi.pdf", psizey = 0.4,}local multi2 = myplot { sid = multi1.sid, originy = 0.4, psizey = 0.4, psizex = 0.5, output = "plot-multi.pdf",}multi2 { epilog = "unset multiplot\n unset out", originx = 0.5,}

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Plot example (LHC 1 & 2 survey)

!11

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!11

plot { sequence = lhc, !{lhcb1,lhcb2} laypos = "in", layonly = false, title = "Layout in plot", prolog = 'set size ratio -1', scrdump = "plotlhc.gp",}

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!11

plot { sequence = lhc, !{lhcb1,lhcb2} laypos = "in", layonly = false, title = "Layout in plot", prolog = 'set size ratio -1', scrdump = "plotlhc.gp",}

Gnuplot script

size of 5 MB & 125355 lines

~1 sec to display

all items are tagged

i.e. moving the mouse over

show their name and kind

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Plot example (LHC 1 & 2 at IP1 & IP5)

!12

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!12

plot { sequence = { lhcb1, lhcb2, lhcb1, lhcb2 }, range = { {“E.DS.L1.B1","S.DS.R1.B1"},{"E.DS.L1.B2","S.DS.R1.B2"}, {"E.DS.L5.B1","S.DS.R5.B1"},{"E.DS.L5.B2","S.DS.R5.B2"}, }, seqdisty = { lhcb2[“E.DS.L1.B2"].mech_sep, ! second bline -0.4, ! third bline -0.4 + lhcb2[‘E.DS.L5.B2'].mech_sep ! fourth bline }, title = "IP1-IP5 two angled beams",}

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!12

plot { sequence = { lhcb1, lhcb2, lhcb1, lhcb2 }, range = { {“E.DS.L1.B1","S.DS.R1.B1"},{"E.DS.L1.B2","S.DS.R1.B2"}, {"E.DS.L5.B1","S.DS.R5.B1"},{"E.DS.L5.B2","S.DS.R5.B2"}, }, seqdisty = { lhcb2[“E.DS.L1.B2"].mech_sep, ! second bline -0.4, ! third bline -0.4 + lhcb2[‘E.DS.L5.B2'].mech_sep ! fourth bline }, title = "IP1-IP5 two angled beams",}

Layout can be at

top, bottom, middle, inside

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Plot example (two rings with 𝜷x)

!13

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Plot example cont’d (two rings with 𝜷x)

!14

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local ncell = 25local mb = sbend { l=2, k0 =\s s.angle/s.l }local mq = quadrupole { l=1 }local cell =\a -> sequence { l=10, refer='entry', mq 'mq1' { at=0, k1=0.29601 }, mb 'mb1' { at=2, angle=a*pi/ncell }, mq 'mq2' { at=5, k1=-0.30242 }, mb 'mb2' { at=7, angle=a*pi/ncell }, }local seq1 = sequence 'seq1' { ncell*cell(+1), beam=beam }local seq2 = sequence 'seq2' { ncell*cell(-1), beam=beam }local sv1 = survey { sequence=seq1, nslice=5, implicit=true, atslice=ftrue, mapsave=true }local tw1 = twiss { sequence=seq1, nslice=5, implicit=true, atslice=ftrue }

! compute betx in global frame local bet11 = { x=vector(#sv1), z=vector(#sv1) }local v, scl = vector(3), round(tw1.beta11:max()/5)for i=1,#sv1 do v = sv1.W[i] * v:fill{3+tw1.beta11[i]/scl, 0, 0} bet11.x[i], bet11.z[i] = v[1], v[3]endbet11.x = bet11.x+sv1.xbet11.z = bet11.z+sv1.z

! plot layout of the two rings and betx on ring 1 plot { sequence = { seq1, seq2 }, laypos = "in", layonly = false, title = "Layout in plot with \u{03b2}_x", data = { x=bet11.x, z=bet11.z }, x1y1 = { x = 'z' }, styles = 'lines', xlabel = "x [m]", ylabel = "z [m]", legend = { z = '\u{03b2}_x/'..scl },}

Plot example cont’d (two rings with 𝜷x)

!14

BE Beams Department

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!15

Extra Slides

BE Beams Department

Laur

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Object model (principle and deferred expressions)

!16

qf

mqqd

quadstrait

element

circuitselements

class kind frame

mq.l = 2.10 ; ! variableqf.k1 = 0.05 ; ! variableqd.k1 = -0.06 ; ! variablemq: quadrupole, l := mq.l; ! kindqf: mq , k1 := qf.k1; ! circuitqd: mq , k1 := qd.k1; ! circuitqf1: qf; ! elementqf->k1 = 0.06 ; ! BAD! no update of childrenvalue qf1->k1 ; ! print 0.05 (no lookup)

mq = quad { l = 2.10 } ! kindqf = mq { k1 = 0.05 } ! circuitqd = mq { k1 = -0.06 } ! circuitqf1 = qf {} ! elementqf.k1 = 0.06 ! update strength of ‘qf’ circuitprint(qf1.k1) ! print 0.06 (lookup)

Clone: parents are prototypes used to create children (chained) Read: attributes are sought in the chain of parents (if needed) Write: attributes are set/overridden only in elements (no lookup)

qf1qd1qf2qd2

BE Beams Department

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cern

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๏ MAD-X definition: ➡ children copy attributes

(share expressions, no dynamic lookup).

➡ global workspace.


!16

qf

mqqd

quadstrait

element

circuitselements

class kind frame




qf1qd1qf2qd2

BE Beams Department

Laur

ent D

enia

u, C

ER

N B

E/A

BP,

121

1 G

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a, la

uren

t.den

iau@

cern

.ch




๏ MAD definition: ➡ children inherit attributes

using dynamic lookup. ➡ structured lattice

description, no global. ➡ avoid the need for >90% of the deferred expressions and save many extra variables.


!16

qf

mqqd

quadstrait

element

circuitselements

class kind frame




qf1qd1qf2qd2

BE Beams Department

Laur

ent D

enia

u, C

ER

N B

E/A

BP,

121

1 G

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a, la

uren

t.den

iau@

cern

.ch








!16

qf

mqqd

quadstrait

element

circuitselements

class kind frame




qf1qd1qf2qd2

3 variables + 4 elements + 3 deferred expressions

(+ 1 problem)

BE Beams Department

Laur

ent D

enia

u, C

ER

N B

E/A

BP,

121

1 G

enev

a, la

uren

t.den

iau@

cern

.ch








!16

qf

mqqd

quadstrait

element

circuitselements

class kind frame




qf1qd1qf2qd2

only 4 elements

3 variables + 4 elements + 3 deferred expressions

(+ 1 problem)

be beams department€¦ · be beams department ch!2 plan 1. overview: survey, track, cofind,...

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