62 research outputs found
High order time integrators for the simulation of charged particle motion in magnetic quadrupoles
Magnetic quadrupoles are essential components of particle accelerators like
the Large Hadron Collider. In order to study numerically the stability of the
particle beam crossing a quadrupole, a large number of particle revolutions in
the accelerator must be simulated, thus leading to the necessity to preserve
numerically invariants of motion over a long time interval and to a substantial
computational cost, mostly related to the repeated evaluation of the magnetic
vector potential. In this paper, in order to reduce this cost, we first
consider a specific gauge transformation that allows to reduce significantly
the number of vector potential evaluations. We then analyze the sensitivity of
the numerical solution to the interpolation procedure required to compute
magnetic vector potential data from gridded precomputed values at the locations
required by high order time integration methods. Finally, we compare several
high order integration techniques, in order to assess their accuracy and
efficiency for these long term simulations. Explicit high order Lie methods are
considered, along with implicit high order symplectic integrators and
conventional explicit Runge Kutta methods. Among symplectic methods, high order
Lie integrators yield optimal results in terms of cost/accuracy ratios, but non
symplectic Runge Kutta methods perform remarkably well even in very long term
simulations. Furthermore, the accuracy of the field reconstruction and
interpolation techniques are shown to be limiting factors for the accuracy of
the particle tracking procedures.Comment: 39 pages, 18 figure
Impact of Detector Solenoid on the CLIC Luminosity Performance
In order to obtain the necessary luminosity with a reasonable amount of beam
power, the Compact Linear Collider (CLIC) design includes an unprecedented
collision beam size of {\sigma} = 1 nm vertically and {\sigma} = 45 nm
horizontally. Given the small and very flat beams, the luminosity can be
significantly degraded from the impact of the experimental solenoid field in
combination with a large crossing angle. Main effects include y-x'-coupling and
increase of vertical dispersion. Additionally, Incoherent Synchrotron Radiation
(ISR) from the orbit deflection created by the solenoid field, increases the
beam emittance. A detailed study of the impact from a realistic solenoid field
and the associated correction techniques for the CLIC Final Focus is presented.
In particular, the impact of techniques to compensate the beam optics
distortions due to the detector solenoid main field and its overlap with the
final focus magnets are shown. The unrecoverable luminosity loss due to ISR has
been evaluated, and found to be in the range 4-5 % for the solenoid design
under study.Comment: Preprint of submission to PRSTA
Ensemble reservoir computing for dynamical systems: prediction of phase-space stable region for hadron storage rings
We investigate the ability of an ensemble reservoir computing approach to predict the long-term behaviour of the phase-space region in which the motion of charged particles in hadron storage rings is bounded, the so-called dynamic aperture. Currently, the calculation of the phase-space stability region of hadron storage rings is performed through direct computer simulations, which are resource- and time-intensive processes. Echo State Networks (ESN) are a class of recurrent neural networks that are computationally effective, since they avoid backpropagation and require only cross-validation. Furthermore, they have been proven to be universal approximants of dynamical systems. In this paper, we present the performance reached by ESN based on an ensemble approach for the prediction of the phase-space stability region and compare it with analytical scaling laws based on the stability-time estimate of the Nekhoroshev theorem for Hamiltonian systems. We observe that the proposed ESN approach is capable of effectively predicting the time evolution of the extent of the dynamic aperture, improving the predictions by analytical scaling laws, thus providing an efficient surrogate model.We investigate the ability of an ensemble reservoir computing approach to predict the long-term behaviour of the phase-space region in which the motion of charged particles in hadron storage rings is bounded, the so-called dynamic aperture. Currently, the calculation of the phase-space stability region of hadron storage rings is performed through direct computer simulations, which are resource- and time-intensive processes. Echo State Networks (ESN) are a class of recurrent neural networks that are computationally effective, since they avoid backpropagation and require only cross-validation. Furthermore, they have been proven to be universal approximants of dynamical systems. In this paper, we present the performance reached by ESN based on an ensemble approach for the prediction of the phase-space stability region and compare it with analytical scaling laws based on the stability-time estimate of the Nekhoroshev theorem for Hamiltonian systems. We observe that the proposed ESN approach is capable of effectively predicting the time evolution of the extent of the dynamic aperture, improving the predictions by analytical scaling laws, thus providing an efficient surrogate model
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