Simulation of Luminosity Variation in Experiments with a Pellet Target A.Smirnov, A.Sidorin (JINR, Dubna, Russia)

Contents Luminosity. Ring, beam and target parameters Luminosity variation in experiment with a pellet target Beam heating and cooling Stabilization of the beam emittance: tilt of the electron beam Compensation of ionization energy loss: barrier RF bucket The processes to be simulated Short-term luminosity variation Detector limitations and effective luminosity

Maximum achievable luminosity The antiproton loss rate in the ring If the antiproton storage efficiency stor is about 100% Upper limit of the mean luminosity Experiment with an Internal target limitation for antiproton number Choice of the target type

Antiproton life-time in the ring 1. Single scattering on acceptance angle This process does not limit the target density if ~ 610-6 or A > 40 mmmrad 2. Ionization energy loss The energy loss are distributed according to At E = 8 GeV, Emax = 42 MeV

Ring acceptance on the momentum deviation Effective cooling of the antiprotons Stochastic cooling time in the first approximation does not depend on the deviation Electron cooling is effective at p/p < 10-3 2. Mean energy loss compensation using RF At reasonable RF amplitude the longitudinal acceptance is p/p ~ 10-3

FAIR: Pellet target L  107/5·10-26 = 2·1032 cm-2 s-1 life > 104 s Expected antiproton production rate is about 107 1/s The reaction cross-section is about 50 mbarn The limit for mean luminosity: L  107/5·10-26 = 2·1032 cm-2 s-1 High Energy Storage Ring: The ring circumference is about 574 m, revolution period is 2 s life > 104 s N  1011   4·1015 cm-2 Pellet target

Luminosity of PANDA experiment (high-luminosity mode) Pbar production / loss rate, s-1 1·107 Cross-section of p - pbar, barn 0,05 Mean luminosity, cm-2 s-1 2·1032 Hydrogen density, Atom/cm3 4,26·1022 Pellet size (diameter), mm 0,028 Pellet flux radius, mm 1,25 Distance between pellets, mm 5 Effective target density, cm-2 4·1015 Revolution period, sec 2·10-6 Antiproton number 1·1011 Peak luminosity, cm-2 s-1

Pellet target  = <>thickness Frozen hydrogen density,  Atoms/cm3 4.261022 The pellet radius, rp m 15 The pellet flux radius, rf mm 1.5 Mean distance between pellets, <h> 5 Mean target density <> 1.71016 Mean distance between pellets Flux radius Pellet diameter  = <>thickness

Areal density for Gaussian beam (pellet is in the beam centre) Peak/mean Effective density  in cm  = 1 mm,  = 4·1015 cm-2, Peak/mean = 2.5

The effects leading to the beam heating 1. Scattering on residual gas atoms is negligible if nrg < 109 cm-3 2. Longitudinal heating due to scattering in the target High resolution mode (HR) p ~ 10-4

The effects leading to the beam heating 3. Transverse heating due to scattering in the target 4. Intra-beam scattering In the thermal equilibrium between longitudinal and transverse degrees of freedom in HR (if transverse and longitudinal cooling rates are the same) It is necessary to stabilize the beam emittance at some reasonable level At IBS is negligible

Beam cooling 1. At stochastic cooling one can adjust longitudinal and transverse cooling times independently 2. At electron cooling the cooling times have comparable values for all degrees of freedom D.Reistad et. al., Calculations on high-energy electron cooling in the HESR, Proceedings of COOL 2007, Bad Kreuznach, Germany Intentional misalignment (tilt) of the electron beam is most attractive for stabilization of the emittance value.

Tilt of the electron beam When the misalignment angle reaches a certain threshold value the ions start to oscillate with a certain value of betatron amplitude. Transverse plane Beam profiles Simulations with BETACOOL

Compensation of ionization energy loss: barrier RF bucket Compensation of mean energy loss by RF decreases sufficiently requirements to the cooling power VRF p/p s-s0 t V0 T2 T1 1 2 max ~ 10-3 V ~ 5 kV

The processes to be simulated 1. Interaction with the pellet target based on realistic scattering models 2. Intra-beam scattering at arbitrary ion distribution 3. Stochastic cooling, taking into account nonlinearity of the force at large amplitudes 4. Electron cooling at electron beam misalignment 5. Longitudinal motion at arbitrary shape of the RF voltage To provide benchmarking Simulations using independent codes (BETACOOL, MOCAC) Comparison with experiments (ESR and COSY) Longitudinal motion in Barrier RF buckets, Investigation of electron cooling with electron beam misalignment, Short term luminosity variation with the WASA pellet target

Physical models of Internal target Longitudinal degree of freedom Gaussian model Real (Urban) model ; ; n1, n2 – number of excitation events to different atomic energy levels n3 – number of ionization events x – uniform random number Eloss – mean energy loss, x – Gaussian random Estr – energy fluctuations (straggling) N N DP/P0 DP/P0 DP/P0+Estr DP/P DP/P Eloss Eloss

Transverse degree of freedom Gaussian model Real (plural) model q – rms scattering angle x – Gaussian random numbers c – screening angle N – number of scattering events x – uniform random numbers target target qstr

Average luminosity calculation with BETACOOL code x s Pellet flux for each model particle Number of events: 1) Integration over betatron oscillation 2) Integration over flux width 3) Number of turns per integration step Number of events for model particle Particle probability distribution Realistic models of interaction with pellet Urban + plural scattering

Parameters of COSY experiment WASA@COSY experiment Deuterium beam Momentum, GeV/c 1.2 Energy, MeV/u 177 Particle number 2×1010 Horizontal emittance,  mm mrad 1 Vertical emittance 0.5 Initial momentum spread 2×10-4 Deuterium target Pellet radius, mm 15 Pellet flux radius, mm 2.5 Mean distance between pellets, mm 10 Deuterium density, atom/cm-3 6×1022 COSY Circumference, m 183.4728 Momentum slip factor,  0.533 Horizontal acceptance,  m rad 2.2E-5 Vertical acceptance,  m rad 1E-5 Acceptance on momentum deviation ±1.2×10-3 For benchmarking BETACOOL code data from COSY experiment (2008 and 2009 runs) was used WASA @ COSY Parameters of COSY experiment

Experiments without barrier bucket h = 8 mm d = 0.03 mm The beam momentum spread can be calculated from measured frequency spread

Investigations of electron cooling at COSY 7-11 April 2010 New fast (~ 40 ms) Ionization Profile Monitor Measurements of longitudinal component of the cooling force, Investigation of chromatic instability Possibility to work with Barrier Buckets

Signals from detectors Green and yellow lines are signals from pellet counter Black line is number of particles Other colour lines are signals from different detectors Simulation of particle number on time Simulation of long scale luminosity on time

Designed parameters for PANDA (high-luminosity mode) Momentum, GeV/c 9 RMS momentum spread 1·10-4 Transverse emittance (RMS normalized) 0,4 Average luminosity, cm-2 s-1 2·1032 Detector limit, cm-2 s-1 3·1032 Effective target density, cm-2 4·1015 Pellet velocity, m/s 60 Pellet flux radius, mm 1,25 Pellet size (diameter), µm 28 Distance between pellets, mm 5

Effective luminosity calculation Pellet distribution Pellet distribution Ion beam profile

Short scale luminosity variations Experiment h = 8 mm d = 0.03 mm Simulation h = 0.2 mm d = 0.01 mm

Two variants of detector limit Top cut y Average luminosity Average luminosity Full cut y Effective luminosity x

Effective to average luminosity ratio for different detector limit (high-luminosity mode) Top cut Full cut

Effective to average luminosity ratio for different detector limit (high-resolution mode) Top cut Full cut

Conclusions The choice of the target density depends on the ring acceptance. More strong limitation leading to necessity of the pellet target is RF voltage amplitude Horizontal beam size at the target has to be stabilized at optimum value (transverse overcooling the beam leads to increase the momentum spread due to IBS and large luminosity variations) Vertical beam size determines short-scale luminosity variation and optimum value has to be about inter pellet distance) Current parameters of the beam and target can be optimized. The code development has to be prolonged as well as experimental study at COSY