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Mitglied der Helmholtz-Gemeinschaft Proposition for the Beam Smearing Implementation inside Pandaroot December 10, 2009 T. Randriamalala, J. Ritman and T. Stockmanns Outiline Introduction and Motivation FairPrimaryGenerator Vertex Smearing

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SLIDE 1

Mitglied der Helmholtz-Gemeinschaft

Proposition for the Beam Smearing Implementation inside Pandaroot

December 10, 2009

  • T. Randriamalala, J. Ritman and T. Stockmanns
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SLIDE 2

Outiline

Introduction and Motivation FairPrimaryGenerator Vertex Smearing HESR Beam Properties Beam Smearing Tentative Implementation Conclusion

December 10, 2009

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SLIDE 3

Introduction and Motivation

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SLIDE 4

Introduction and Motivation

Beam smearing can be done by acting on the outgoing generated particles (cf. PCM 09.09 (Smearing of the DPM

  • utpout)).

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SLIDE 5

Introduction and Motivation

Beam smearing can be done by acting on the outgoing generated particles (cf. PCM 09.09 (Smearing of the DPM

  • utpout)).

Similarly, one can operate by using FairPrimaryGenerator (modified).

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SLIDE 6

Introduction and Motivation

Beam smearing can be done by acting on the outgoing generated particles (cf. PCM 09.09 (Smearing of the DPM

  • utpout)).

Similarly, one can operate by using FairPrimaryGenerator (modified). But, the current implementation FairPrimaryGenerator can smear only vertices = ⇒ Angular smearing should be implemented (beam particles do not have identical 4-momemtum)

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SLIDE 7

Introduction and Motivation

Beam smearing can be done by acting on the outgoing generated particles (cf. PCM 09.09 (Smearing of the DPM

  • utpout)).

Similarly, one can operate by using FairPrimaryGenerator (modified). But, the current implementation FairPrimaryGenerator can smear only vertices = ⇒ Angular smearing should be implemented (beam particles do not have identical 4-momemtum) Also, the vertex smearing should be modified according to the HESR beam properties.

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SLIDE 8

FairPrimaryGenerator Vertex Smearing

In the simulation macro:

FairPrimaryGenerator* primGen = new FairPrimaryGenerator(); primGen->SetTarget(0.0, 0.2); primGen->SmearVertexZ(kTRUE); primGen->SetBeam(0.0, 0.0, 0.08, 0.08); primGen->SmearVertexXY(kTRUE); December 10, 2009

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SLIDE 9

FairPrimaryGenerator Vertex Smearing

In the simulation macro:

FairPrimaryGenerator* primGen = new FairPrimaryGenerator(); primGen->SetTarget(0.0, 0.2); primGen->SmearVertexZ(kTRUE); primGen->SetBeam(0.0, 0.0, 0.08, 0.08); primGen->SmearVertexXY(kTRUE); a flat distribution for the Z-position of the vertex with a width of 0.2cm centered on 0.0 X and Y will be smeared both by a gaussian centered on 0.0, with σ = 0.08cm. December 10, 2009

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SLIDE 10

FairPrimaryGenerator Vertex Smearing

In the simulation macro:

FairPrimaryGenerator* primGen = new FairPrimaryGenerator(); primGen->SetTarget(0.0, 0.2); primGen->SmearVertexZ(kTRUE); primGen->SetBeam(0.0, 0.0, 0.08, 0.08); primGen->SmearVertexXY(kTRUE); a flat distribution for the Z-position of the vertex with a width of 0.2cm centered on 0.0 X and Y will be smeared both by a gaussian centered on 0.0, with σ = 0.08cm.

Run a simulation:

fRun->SetGenerator(primGen); FairBoxGenerator* boxGen =... boxGen->SetXYZ(0., 0., 0.); primGen->AddGenerator(boxGen); December 10, 2009

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SLIDE 11

Smearing Output

Before vertex smearing After vertex smearing

Entries 5000 Mean RMS x [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 1000 2000 3000 4000 5000 Entries 5000 Mean RMS Entries 5000 Mean RMS y [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 1000 2000 3000 4000 5000 Entries 5000 Mean RMS Entries 5000 Mean RMS z [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 1000 2000 3000 4000 5000 Entries 5000 Mean RMS Entries 5000 Mean −0.001164 RMS 0.07979 x [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 Entries 5000 Mean −0.001164 RMS 0.07979 Entries 5000 Mean −0.00129 RMS 0.08051 y [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 Entries 5000 Mean −0.00129 RMS 0.08051 Entries 5000 Mean 0.0007176 RMS 0.05748 z [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 300 Entries 5000 Mean 0.0007176 RMS 0.05748

1 D. Reistad, B. Galnander, K. Rathsman, A. Sidorin, "Calculations on High-Energy Electron Cooling in the HESR", Proceedings of COOL 2007, Bad Kreuznach. and V.Ziemann, NIMA 556 (2006) 641. December 10, 2009

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SLIDE 12

Smearing Output

Before vertex smearing After vertex smearing

Entries 5000 Mean RMS x [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 1000 2000 3000 4000 5000 Entries 5000 Mean RMS Entries 5000 Mean RMS y [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 1000 2000 3000 4000 5000 Entries 5000 Mean RMS Entries 5000 Mean RMS z [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 1000 2000 3000 4000 5000 Entries 5000 Mean RMS Entries 5000 Mean −0.001164 RMS 0.07979 x [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 Entries 5000 Mean −0.001164 RMS 0.07979 Entries 5000 Mean −0.00129 RMS 0.08051 y [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 Entries 5000 Mean −0.00129 RMS 0.08051 Entries 5000 Mean 0.0007176 RMS 0.05748 z [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 300 Entries 5000 Mean 0.0007176 RMS 0.05748

This should be treated differently according the HESR beam properties 1

1 D. Reistad, B. Galnander, K. Rathsman, A. Sidorin, "Calculations on High-Energy Electron Cooling in the HESR", Proceedings of COOL 2007, Bad Kreuznach. and V.Ziemann, NIMA 556 (2006) 641. December 10, 2009

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SLIDE 13

Smearing Output

Before vertex smearing After vertex smearing

Entries 5000 Mean RMS x [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 1000 2000 3000 4000 5000 Entries 5000 Mean RMS Entries 5000 Mean RMS y [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 1000 2000 3000 4000 5000 Entries 5000 Mean RMS Entries 5000 Mean RMS z [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 1000 2000 3000 4000 5000 Entries 5000 Mean RMS Entries 5000 Mean −0.001164 RMS 0.07979 x [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 Entries 5000 Mean −0.001164 RMS 0.07979 Entries 5000 Mean −0.00129 RMS 0.08051 y [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 Entries 5000 Mean −0.00129 RMS 0.08051 Entries 5000 Mean 0.0007176 RMS 0.05748 z [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 300 Entries 5000 Mean 0.0007176 RMS 0.05748

This should be treated differently according the HESR beam properties 1 + angluar smearing

1 D. Reistad, B. Galnander, K. Rathsman, A. Sidorin, "Calculations on High-Energy Electron Cooling in the HESR", Proceedings of COOL 2007, Bad Kreuznach. and V.Ziemann, NIMA 556 (2006) 641. December 10, 2009

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SLIDE 14

Antiproton Beam Properties

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Antiproton Beam Properties

At the IP , the emittance ε of the ¯ p-beam is 1 mm mrad .

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SLIDE 16

Antiproton Beam Properties

At the IP , the emittance ε of the ¯ p-beam is 1 mm mrad . ε = 2σx · 2σθ

σx : RMS of the transversal divergance of the beam. σθ : RMS of the angular divergance of the beam.

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SLIDE 17

Antiproton Beam Properties

At the IP , the emittance ε of the ¯ p-beam is 1 mm mrad . ε = 2σx · 2σθ

σx : RMS of the transversal divergance of the beam. σθ : RMS of the angular divergance of the beam.

For σx ≤ 0.8mm, Leff ≥ 0.8Lmax because of the beam-target overlap (pellet target).

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SLIDE 18

Vertex Smearing

Event-by-event smearing:

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SLIDE 19

Vertex Smearing

Event-by-event smearing: Choose σx = σy = 0.8mm.

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SLIDE 20

Vertex Smearing

Event-by-event smearing: Choose σx = σy = 0.8mm. If σx ≤ 0.5 × R = ⇒ Homogeneous "square" distribution of ¯ p in the beam with a side of (2 × σx). where R is the cross section radius of the pellet flux (R ∼ 2mm).

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SLIDE 21

Vertex Smearing

Event-by-event smearing: Choose σx = σy = 0.8mm. If σx ≤ 0.5 × R = ⇒ Homogeneous "square" distribution of ¯ p in the beam with a side of (2 × σx). where R is the cross section radius of the pellet flux (R ∼ 2mm). Gaussian smearing in the z-direction with σz = R/2 = 1mm.

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SLIDE 22

Angular Smearing

For the 3-momentum vectors pi (i = {p, ¯ p}):

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SLIDE 23

Angular Smearing

For the 3-momentum vectors pi (i = {p, ¯ p}): Rotation of δθ around ˆ n =

  • pi׈

k | pi|·|ˆ k| (ˆ

k(0, 0, 1).) δθ is a Gaussian distribution with σθ = 0.3mrad. (δθ must be positive numbers.)

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SLIDE 24

Angular Smearing

For the 3-momentum vectors pi (i = {p, ¯ p}): Rotation of δθ around ˆ n =

  • pi׈

k | pi|·|ˆ k| (ˆ

k(0, 0, 1).) δθ is a Gaussian distribution with σθ = 0.3mrad. (δθ must be positive numbers.) Rotation of δϕ around pi. δϕ is an uniform distribution [−π, +π].

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SLIDE 25

Angular Smearing

For the 3-momentum vectors pi (i = {p, ¯ p}): Rotation of δθ around ˆ n =

  • pi׈

k | pi|·|ˆ k| (ˆ

k(0, 0, 1).) δθ is a Gaussian distribution with σθ = 0.3mrad. (δθ must be positive numbers.) Rotation of δϕ around pi. δϕ is an uniform distribution [−π, +π]. No correlation between δθ and δϕ.

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SLIDE 26

Before smearing After smearing

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Tentative Implementation

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SLIDE 28

Tentative Implementation

In FairPrimaryGenerator class:

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SLIDE 29

Tentative Implementation

In FairPrimaryGenerator class:

change the flat distribution on Z to a gaussian.

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Tentative Implementation

In FairPrimaryGenerator class:

change the flat distribution on Z to a gaussian. change the gaussian distributions on X and Y to an uniform.

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SLIDE 31

Tentative Implementation

In FairPrimaryGenerator class:

change the flat distribution on Z to a gaussian. change the gaussian distributions on X and Y to an uniform. introduce the angular smearing

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SLIDE 32

Tentative Implementation

In FairPrimaryGenerator class:

change the flat distribution on Z to a gaussian. change the gaussian distributions on X and Y to an uniform. introduce the angular smearing

In simulation macro, add: primGen->SetAngularDivergence(0.3*1E-3); primGen->SmearAngle(kTRUE);

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SLIDE 33

Tentative Implementation

In FairPrimaryGenerator class:

change the flat distribution on Z to a gaussian. change the gaussian distributions on X and Y to an uniform. introduce the angular smearing

In simulation macro, add: primGen->SetAngularDivergence(0.3*1E-3); primGen->SmearAngle(kTRUE); Use FairBoxGenerator to generate event (5000 event, 1 particle/event)

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Results

Effect of the modification on the vertex (bottom plots) in comparison with the existing one (top plot):

Entries 5000 Mean −0.001164 RMS 0.07979

x [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250

Entries 5000 Mean −0.001164 RMS 0.07979 Entries 5000 Mean −0.00129 RMS 0.08051

y [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250

Entries 5000 Mean −0.00129 RMS 0.08051 Entries 5000 Mean 0.0007176 RMS 0.05748

z [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 300

Entries 5000 Mean 0.0007176 RMS 0.05748 Entries 5000 Mean 0.0005527 RMS 0.0461

x [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 300 350

Entries 5000 Mean 0.0005527 RMS 0.0461 Entries 5000 Mean 0.0002616 RMS 0.04613

y [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 50 100 150 200 250 300

Entries 5000 Mean 0.0002616 RMS 0.04613 Entries 5000 Mean 0.0008109 RMS 0.09911

z [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 20 40 60 80 100 120 140 160 180 200 220 240

Entries 5000 Mean 0.0008109 RMS 0.09911

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Angular divergence distribution:

Entries 5000 Mean 0.0002388 RMS 0.0001777 theta [rad] −0.002 −0.0015 −0.001 −0.0005 0 0.00050.0010.00150.002 100 200 300 400 500 Entries 5000 Mean 0.0002388 RMS 0.0001777 Entries 5000 Mean 0.006993 RMS 1.812 phi [rad] −4 −3 −2 −1 1 2 3 4 20 40 60 80 100 Entries 5000 Mean 0.006993 RMS 1.812

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Angular divergence distribution: Beam profile in xy plane at 1m from the IP:

Entries 5000 Mean 0.0002388 RMS 0.0001777 theta [rad] −0.002 −0.0015 −0.001 −0.0005 0 0.00050.0010.00150.002 100 200 300 400 500 Entries 5000 Mean 0.0002388 RMS 0.0001777 Entries 5000 Mean 0.006993 RMS 1.812 phi [rad] −4 −3 −2 −1 1 2 3 4 20 40 60 80 100 Entries 5000 Mean 0.006993 RMS 1.812

x [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 y [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4

Entries 5000 Mean x −0.001164 Mean y −0.00129 RMS x 0.07979 RMS y 0.08051 Entries 5000 Mean x −0.001164 Mean y −0.00129 RMS x 0.07979 RMS y 0.08051

x [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 y [cm] −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4

Entries 5000 Mean x 0.0005547 Mean y 0.0002623 RMS x 0.04611 RMS y 0.04614 Entries 5000 Mean x 0.0005547 Mean y 0.0002623 RMS x 0.04611 RMS y 0.04614

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SLIDE 37

Conclusion

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SLIDE 38

Conclusion

Pandaroot provides a beam smearing tool.

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SLIDE 39

Conclusion

Pandaroot provides a beam smearing tool. Some change need to be considered : vertex and angular smearing distribution,

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SLIDE 40

Conclusion

Pandaroot provides a beam smearing tool. Some change need to be considered : vertex and angular smearing distribution, If ε = 1 mm mrad, the resolution of one subdetector is affected ( δθ ≥ 0.3mrad for the LM ).

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