LHC Collimation Working Group – 19 December 2011

Modeling and Simulation of Beam Losses during

Collimator Alignment

(Preliminary Work)

G. Valentino

With input from: R.W. Assmann, R. Bruce, F. Burkart, S. Redaelli,

A. Rossi, D. Wollmann

Outline

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• Introduction

• Motivation for Modeling and Simulation of Beam Losses during Setup

• Modeling of Beam Losses Gaussian beam distribution model

Parametric modeling of the beam loss temporal decay

• Simulator Algorithm

• Summary and Future Work

Introduction

• The collimators are aligned using beam-based alignment.

• Each jaw is moved in towards the beam until a loss spike is recorded on a BLM.

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BLM Signal

Left Jaw

Right Jaw

Parameters such as jaw step size and loss threshold affect loss spike quality

• However, the loss spikes are not always so clear:

Loss Spike Structure

• 4 components: background (1), loss spike, loss decay, background (2)

• This work addresses only the spike and decay.

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Background (1)

Loss Spike

Background (2)

Temporal Decay

Motivation for Modeling and Simulation of Beam Losses

during Setup

• To allow offline tests of automatic setup algorithms without requiring beam.

• To compare the measured beam losses to those predicted by existing models.

• To understand and parameterize the temporal decay in losses which is not yet fully understood.

• A better understanding of the beam losses during collimator setup will allow for a more accurate automation of the setup procedure.

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Gaussian Beam Distribution Model

• Paper: Intensity and Luminosity after Beam Scraping (H. Burkhardt & R. Schmidt)

• Fraction of particles lost:

• Distribution after cut of :

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Courtesy of H. Burkhardt and R. Schmidt

€

Fl (nσ ) = e−nσ

2

2 = e

−1

2(x−x0 )2

σ x2

€

y =e

−x 2

2σ 2

2πerf

nσ2 −x 2

σ x2

2

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟

× N0- Beam cut

(sigmas)- Jaw position

(mm)- Beam centre

(mm)- 1 beam sigma

(mm)- Intensity

€

x0

€

x

€

σx€

nσ

€

N0

Measured vs Simulated Intensity

• 40 µm steps every 4 seconds, beam scraping MD (450 GeV)

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Initial Intensity: 1.2400E11Lost Measured Intensity: 1.2702E11Lost Simulated Intensity: 1.2397E11

Centre: 0.470 mm

Intensity Lost every 4 seconds

Intensity Remaining every 4 seconds

Centre: 0.470 mm

Errors in the Model• Model assumes that after the jaw is moved in and the tail particles are

scraped away, the tail population at the jaw position decays to 0.

• In reality, the losses decay to a constant loss rate (tail repopulation), which increases as the jaw moves further into the beam.

• Additionally, Gaussian distribution model for the tails is imperfect (also shown by F. Burkart)

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Jaw Position (1)

Jaw Position (2)

Jaw Step Size exaggerated

(typically ~10µm)

Initial Distribution at (1)

Actual Distribution at (2)

Assumed Distribution at (2)

Error Compensation

• Model assumes that there are no losses before jaw movement, so approximate measured data by “subtracting” some losses:

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Initial Intensity: 1.2400E11Lost Measured Intensity: 1.2702E11Lost Simulated Intensity: 1.2394E11

Shift in Peak

Intensity Lost every 4 seconds

Intensity Remaining every 4 seconds

€

Fl (nσ ) = e

−1

2(x−x0 )2

σ x2

− e

−1

2(x+0.15−x0 )2

σ x2

Chosen for best fit to measured data

Converting Loss Rate to BLM Signal

• BLM signal (Gy/s) can be obtained from the loss rate (p/s) via the calibration factor (~1.25E11)

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€

Sblmi (t) =

Ri(t)

fcalibi F. Burkart et al. IPAC’11

Maximum BLM Value every 4 seconds

Parametric Modeling of Temporal Loss Decay

• Attempt to fit an exponential curve to the temporal loss decay.

• Number of samples: 299 at 450 GeV, 262 at 3.5 TeV (collimator setup data).

• Fit parameters: Amplitude a

Power coefficient n

Error between fit and data R

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Temporal Decay from Scraping MD too short for analysis

Parametric Modeling Results (1)

• In addition, all samples were visually examined to determine the decay time.

• No correlations observed between e.g. step size and spike height, half gap and decay time, …

• Precautions are taken during setup to achieve uniform loss spikes and losses below the dump threshold.

• E.g. 10 µm jaw step every 3 seconds (instead of every 1 second).

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Parameter 450 GeV 3.5 TeV

Jaw Step Size (µm)

10 – 20 5 – 10

Decay Time (s) 5.22 ± 2.71 7.86 ± 2.59

Amplitude a (Gy/s)

1.29E-05 ± 1.70E-05

1.22E-05 ± 1.78E-05

Power coefficient n

- 0.747 ± 0.367 - 0.571 ± 0.257

Error coefficient R

0.887 ± 0.121 0.927 ± 0.103

Parametric Modeling Results (2)

• Fit log-normal curves to (absolute) power coefficients at 450 GeV and 3.5 TeV:

• Power coefficients can be drawn randomly from the log-normal distribution with parameters µ and σ depending on the energy.

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Combining Gaussian & Parametric Models

• The simulated BLM signal in time can be obtained by combining both models.

• Loss spike generated by converting lost intensity into Gy/s using calibration factor.

• Temporal decay obtained from spike amplitude and the randomly-drawn power coefficient.

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Discrepancy between measurements and model

Simulator Algorithm

Initialization:

• Randomize beam centres (from real data) by ± 200 µm.

• Calculate beam size at the collimators for a given emittance.

For every collimator jaw movement:

1. Calculate fraction of particles lost.

2. Convert into BLM signal using calibration factor.

3. Calculate new beam distribution and get new sigma from fit.

4. Decrease the intensity.

5. Randomly choose power coefficient from log-normal distribution and plot BLM decay until the jaw remains stationary.

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Summary and Future Work

• Preliminary model appears to compare well to measured data.

• Tails are more populated than expected from Gaussian distribution model.

• More data will be analyzed e.g. TOTEM scraping data to try to observe correlations between different parameters e.g. step size & spike height, half gap & decay time

• Other effects need to be modeled, e.g. cross-talk during parallel collimator setup, increase in background losses.

• Simulator does not need to be perfect, but must produce realistic loss spikes and temporal decay for setup algorithm testing.

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