Contents 1 Introduction 2 Magnetic field calculation inside ALICE detector 3 Methods 4 Results 5 Discussions 6 Conclusion

Transcription

1 O 2 O 2

2 O(1) O(1)

3 T n O 2 50MeV /c (x, y, z) B x Z = 0 25 Z 30 Z = 0

4 B y Z = 0 25 Z 30 Z = 0 ϕ Z = 5, 0, 5 a = ax + b 1760 Z Z Z zid = 0 zid = 88

5 p T s = B z = 5e 03

6 D 0 K π + Λ + c pk π + O 2 > 1/ K t =

7

8 Temperature (MeV) Primordial Universe (<10-6 s) Quark-Gluon Plasma 150 Hadronic gas 100 p K 50 "Ordinary" state "Solid" state Phase Transition Neutron Stars Net baryonic density (normalised, d/d 0 ) p

9 10nb 1 (B = 0.5 3nb 1 B = nb 1 R AA v 2 D s p T Λ c R AA v 2 20 Λ c /D R AA v 2 D 0

10 Observable Approved Upgrade p Amin T statistical p Umin T statistical (GeV/c) uncertainty (GeV/c) uncertainty Heavy Flavour D meson R AA 1 10 %at p Amin T %at p Amin T D meson from B decays R AA 3 30 %at p Amin T 2 1%at p Amin T D meson elliptic flow 1 50 %at p Amin T %at p Amin T D meson from B elliptic flow not accessible 2 20 %at p Umin T Charm baryon-to-meson ratio not accessible 2 15 %at p Umin T D s meson R AA 4 15 %at p Amin T 1 1%at p Amin T Charmonia J/ψ R AA (forward rapidity) 0 1 % at 1 GeV/c %at 1GeV/c J/ψ R AA (mid rapidity) 0 5 % at 1 GeV/c %at 1GeV/c J/ψ elliptic flow 0 15 % at 2GeV/c 0 5% at 2GeV/c ψ(2s) yield 0 30 % 0 10 % Dielectrons Temperature (intermediate mass) not accessible 10 % Elliptic flow not accessible 10 % Low-mass spectral function not accessible % Heavy Nuclear States Hyper(anti)nuclei 4 ΛH yield 35 % 3.5 % Hyper(anti)nuclei 4 ΛΛH yield not accessible 20 % p T

11 B + D 0 π + 10 Λ b p T > 7 R AA J/ψ p T = 0 1 R AA ψ(2s) p T = 0 10 v 2 J/ψ p T = O 2 O 2

12 S/ev S/B B /ev D 0 K π D s + K + K π < > 4.6 Λ + c pk π < 10 4 > 26 Λ + c pk π + (p > 2/c) s = 5.5 Adjusted accounting for current luminosity Adjusted with multiplicity procedures multiplicity refittng calorimeters Vertexing matching PID calibrations Local processing clusterization finding DCS data trigg association) CTF AOD Step 0 Step 1 Step 2 Step 3 Step 4 O 2

13 Detectors Switching Storage 250 FLPs 1500 EPNs Network Network 34 Storage Servers Storage 1.1 TB/s 500 GB/s 90 GB/s 8300 Readout Links Input: 250 ports Output : 1500 ports 1500 x 60MB/s

14 50MeV /c

15 O 2 ±10 3 B z B z = 2, 5 O 2

16 O

17 (x, y, z) (B x, B y, B z ) (x, y, z) (x, y, z)

18 B z bz = c[0] + c[1] z + c[2] r + c[3] z z + c[4] z r + c[5] r r; c φ B z B x, B y φ 10 3 B z B(x, y, z) (r, ϕ, z) ϕ

19 B x B x = w 0 + w 1 x 1 + w 2 x 2 + w 3 x w m x m = w x w i R w (w 0, w 1,..., w m ) x (x 1, x 2,..., x m ) x = (x, y, z) x 2, xy, z 2 x B x B x (x, y, z) = a 0 + a 1 x + a 2 y + a 3 z + a 4 xx + a 5 xy + a 6 xz + a 7 yy + a 8 yz + a 9 zz + a 10 xxx + a 11 xxy + a 12 xxz + a 13 xyy + a 14 xyz + a 15 xzz + a 16 yyy + a 17 yyz + a 18 yzz + a 19 zzz w = (a 0, a 1,..., a 19 ) x B x (x, y, z) = a 0 + x(a 1 + x(a 4 + xa 10 + ya 11 + za 12 ) + y(a 5 + za 14 )) + y(a 2 + y(a 7 + xa 13 + ya 16 + za 17 ) + z(a 8 )) + z(a 3 + z(a 9 + xa 15 + ya 18 + za 19 ) + x(a 6 )) N B x i x i, B x,i w

20 R R = 0 (R 80 ) (80 < R 250) (250 < R 400) (400 < R 423) (423 < R 500) r = x 2 + y 2 x 2 + y 2 ϕ ϕ ϕ Z B x, B y Z = 0 ϕ Z = 0

21 B x Z = 0 25 Z 30 Z = z () = 440

22 B y Z = 0 25 Z 30 Z = 0 ϕ Z = 5, 0, 5 x, y, z B x, B y, B z (B x, B y, B z ) B z (B x, B y, B z ) B z B z (x, y, z)

23 B z 1 + 2x + 3x 2 + 4x x(2 + x(3 + 4x)) x ax+b O 2 O 2 a = ax + b O(1) O( n) n 90 < 2 7

24 _dip5k1bz: pushq %rbp movq %rsp, %rbp movss (%rdi), %xmm0 movss 4(%rdi), %xmm3 movss 8(%rdi), %xmm1 movss (%rip), %xmm2 mulss %xmm3, %xmm2 addss (%rip), %xmm2 movss (%rip), %xmm4 mulss %xmm3, %xmm4 addss (%rip), %xmm4 movss (%rip), %xmm5 mulss %xmm1, %xmm5 addss %xmm4, %xmm5 movss (%rip), %xmm4 mulss %xmm0, %xmm4 addss (%rip), %xmm4 mulss (%rip), %xmm3 addss %xmm4, %xmm3 movss (%rip), %xmm4 mulss %xmm1, %xmm4 addss %xmm3, %xmm4 mulss %xmm0, %xmm4 addss %xmm5, %xmm4 mulss %xmm0, %xmm4 addss %xmm2, %xmm4 movss (%rip), %xmm0 mulss %xmm1, %xmm0 addss (%rip), %xmm0 mulss %xmm1, %xmm0 addss (%rip), %xmm0 mulss %xmm1, %xmm0 addss (%rip), %xmm0 mulss %xmm1, %xmm0 addss %xmm4, %xmm0 popq %rbp retq _dip5k1bz: pushq %rbp movq %rsp, %rbp vmovss (%rdi), %xmm0 vmovss 4(%rdi), %xmm1 vmovss 8(%rdi), %xmm2 vmovss (%rip), %xmm3 vfmadd213ss (%rip), %xmm1, %xmm3 vmovss (%rip), %xmm4 vfmadd213ss (%rip), %xmm1, %xmm4 vfmadd231ss (%rip), %xmm2, %xmm4 vmovss (%rip), %xmm5 vfmadd213ss (%rip), %xmm0, %xmm5 vfmadd231ss (%rip), %xmm1, %xmm5 vfmadd231ss (%rip), %xmm2, %xmm5 vfmadd213ss %xmm4, %xmm0, %xmm5 vfmadd213ss %xmm3, %xmm0, %xmm5 vmovss (%rip), %xmm0 vfmadd213ss (%rip), %xmm2, %xmm0 vfmadd213ss (%rip), %xmm2, %xmm0 vfmadd213ss (%rip), %xmm2, %xmm0 vfmadd213ss %xmm5, %xmm2, %xmm0 popq %rbp retq nopw %cs:(%rax,%rax) a = ax + b

25 O(n) O ( n) O (n) 1760 Z zid = 0 zid = 88 O(1) z z min z max width = z max z min number of divisions offset = z min z

26 Z (cm) 1760 Z Z Z zid = 0 zid = 88

27 z Z index (z offset) (number of divisions/width). index > number of divisions search failed. slice slices[index]. id former zid of slice +( z < segment end position of slice 0 1). id. index = 6 0 index < number of divisions slices segment end position zid former zid segment end position = + zid zid + 1 zid z zid = 3 zid

28 n 1 while(true){ maxsegments 0 lastzid 0 for(i 0; i < n; + + i){ slice start i (width/n) + offset slice end (i + 1) (width/n) + offset nsegs 0 slices[i] (lastzid, +inf) for(j 0; j < segends.length; + + j) if(slice start < segends[j] < slice end) nsegs + + slices[i] (j, segends[j]) lastzid j maxsegments max(maxsegments, nsegs) if(maxsegments == 1)return(n, slices) n + +

29 µ/ n n Z Z > 240 φ, Z Z Z > 250

30 Z ΔB x, kgauss ΔB x ALICE performance ΔB x, kgauss ΔB x ALICE performance ΔB x, kgauss Bx ALICE performance ϕ R, cm ΔB y, kgauss ΔB y ΔB y, kgauss ΔB y ΔB y, kgauss B y ϕ Z R, cm ΔB z, kgauss ΔB z ΔB z, kgauss ΔB z ΔB z, kgauss B z ϕ ALI PERF ALI PERF Z ALI PERF R, cm

31

32 r p ϕ

33 R Bz = 5e 03

34 = 440 B z 10 3

35 O(1)

36 T n T 0 (x) = 1 T 1 (x) = x T n+1 (x) = 2xT n (x) T n 1 (x) T 0 (x) = 1 T 1 (x) = x T 2 (x) = 2x 2 1 T 3 (x) = 4x 3 3x T 4 (x) = 8x 4 8x T 5 (x) = 16x 5 20x 3 + 5x T 6 (x) = 32x 6 48x x 2 1 T 7 (x) = 64x 7 112x x 3 7x T 8 (x) = 128x 8 256x x 4 32x T 9 (x) = 256x 9 576x x 5 120x 3 + 9x T 10 (x) = 512x x x 6 400x x 2 1 T 11 (x) = 1024x x x x x 3 11x T n n

37 p j A i,j (i = x, y, z) B i,j B i = 1 N N B i,j A i,j j=1 RMS( B i ) = 1 N N (B i,j A i,j ) 2 j=1 ( B) = B i,j A i,j j Samples B z 10 3

38 (* Cheb: A piece of scalar parametrization *) Cheb[p_, {r_, ϕ_, z_}] := Length[p] j=1 Lengthpj k=1 ChebyshevT[j - 1, r]; Lengthpj,k -p[[j, k, l]] ChebyshevT[l - 1, z] ChebyshevT[k - 1, ϕ] l=1 (* Inbox: Point (r,φ,z) b or not *) InBox[b_] := Thread[Between[{r, ϕ, z}, MapThread[List, b]]]; (* Cheb3D: A pair of 3 params (Bx,By,Bz) and its interpolation region *) Cheb3D[block_] := {Cheb[block[["interpolationOutputs", #, "chebyshevpolynomialcoeffs"]], RescalingTransform[block[["interpolationRegion"]] // Transpose, {{-1, 1}, {-1, 1}, {-1, 1}}][ {r, ϕ, z}]], InBox[block[["interpolationRegion"]]]} & /@ {1, 2, 3}; (* AliMagWrapCheb: Create a 3D-field parametrization *) AliMagWrapCheb[cheb_] := Piecewise /@ (Cheb3D /@ cheb // Transpose); (* AliMagF: Naive reimplementation of AliMagF#Field() *) AliMagF[measurement_, param_] := If[param == "dipoleparams", # /. {r x, ϕ y} &, TransformedField["Cylindrical" "Cartesian", #, {r, ϕ, Null} {x, y, z}] &] /@ AliMagWrapCheb[Import[measurement, "RawJSON"][[2, param, All, 2]]]; (* Usage *) sol = AliMagF["Sol30_Dip6_Hole.json", "solenoidparams"]; sol /. {x 0, y 0, z 0} dip = AliMagF["Sol30_Dip6_Hole.json", "dipoleparams"]; dip /. {x 0, y 0, z -1000}

39 (* Cheb: A piece of scalar parametrization *) Cheb[p_, {r_, ϕ_, z_}] := Length[p] j=1 Lengthpj k=1 ChebyshevT[j - 1, r]; Lengthpj,k -p[[j, k, l]] ChebyshevT[l - 1, z] ChebyshevT[k - 1, ϕ] l=1 (* Cheb3D: A pair of 3 params (Bx,By,Bz) and its interpolation region *) Cheb3D[block_] := {Cheb[block[["interpolationOutputs", #, "chebyshevpolynomialcoeffs"]], RescalingTransform[(block[["interpolationRegion"]] // Transpose), {{-1, 1}, {-1, 1}, {-1, 1}}][ {x, y, z}]], block[["interpolationregion"]]} & /@ {1, 2, 3}; (* ExpandPower: Replace Power[y,2] to (y*y) *) ExpandPower[e_] := StringReplace[ToString[CForm[ e //. Power[y_, n_] StringJoin["(", Riffle[Table[SymbolName[y], n], "*"], ")"] ]], {" " "", "\"" ""}]; (* remove unneeded characters *) (* CHornerForm: Encode a polynomial to C-like efficient form *) CHornerForm[e_] := ExpandPower[HornerForm[e]]; fieldtemplate = StringTemplate[ "void ``(const float p[3], float b[3]) { const float x = p[0], y = p[1], z = p[2]; b[0] = ``; b[1] = ``; b[2] = ``bz(p); };"]; bztemplate = StringTemplate[ "float ``bz(const float p[3]) { const float x = p[0], y = p[1], z = p[2]; return ``; };"]; (* ChebCodeGen: Write C functions to be used with Field() and GetBz() *) ChebCodeGen[hornered_, prefix_] := StringRiffle[MapIndexed[ Module[{funcname = prefix <> ToString[First[#2] - 1]}, bztemplate[funcname, #1[[2, 3]]] <> "\n" <> fieldtemplate[funcname, #1[[2, 1]], #1[[2, 2]], funcname]] &, hornered], "\n\n"]; (* PrepareFastDipoleData: Take a jsonified AliMagWrapCheb data and write dipole parametrizations *) PrepareFastDipoleData[jsonFilePath_, exportfilepath_, prefix_] := Module[{data = Import[jsonFilePath, "RawJSON"]}, Module[{dipole = Cheb3D /@ data[[2, "dipoleparams", All, 2]]}, Module[ {hornered = Map[{(*region*)#[[1, 2]], (*Bx,By,Bz*)CHornerForm /@ #[[All, 1]]} &, dipole]}, Export[exportFilePath, ChebCodeGen[hornered, prefix], "String"] ]]]; AliRootGit = "alice/aliroot"; AliPhysicsGit = "alice/aliphysics"; SourceFile[name_] := FileNameJoin[{$HomeDirectory, AliPhysicsGit, "PWGPP/FieldParam", name}]; DestFile[name_] := FileNameJoin[{$HomeDirectory, AliRootGit, "data/maps", name}]; PrepareFastDipoleData[SourceFile["Sol12_Dip6_Hole.json"], DestFile["dip2k.c"], "dip2k"] PrepareFastDipoleData[SourceFile["Sol30_Dip6_Hole.json"], DestFile["dip5k.c"], "dip5k"]