IPAC2012 - List of Authors (Erdelyi, B.)

Paper	Title	Page
MOEPPB006	Formation of Beams in the Ion Accelerator Complex of the Medium Energy Electron Ion Collider Facility at JLab	88
	S.L. Manikonda, P.N. Ostroumov ANL, Argonne, USA B. Erdelyi Northern Illinois University, DeKalb, Illinois, USA
	Funding: This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. DE-AC02-06CH11357. At the interaction point of the Medium Energy Electron Ion Collider (MEIC) facility the luminosity of 10³³cm^-2s^-1 will be achieved through the collision of counter rotating beams of 0.5A ions and 3A electrons at 750MHz frequency. Formation of ion beams at MEIC is carried out in the Ion Accelerator Complex (IAC) comprising of a linac, pre-booster ring, booster ring, and a collider ring. We will describe the scheme proposed for the formation of ion beams at MEIC facility from the point of view of longitudinal beam dynamics. The proposed scheme minimizes losses due to space charge effects at low energies and needs moderate RF requirements already achieved at other existing facilities. Simulation studies have been conducted to verify the proposed scheme. We will present the results of these simulation studies.

MOPPC093	Optimal Fast Multipole Method Data Structures	352
	S. Abeyratne, B. Erdelyi Northern Illinois University, DeKalb, Illinois, USA S.L. Manikonda ANL, Argonne, USA
	The Fast Multipole Method (FMM) has been identified as one of the ten most significant numerical algorithms discovered in the 20th century. The FMM guarantees finding fast solutions to many problems in science, such as calculating Coulomb potentials among large number of particles by reducing memory footprint and run time while attaining very high accuracy levels. One important practical issue that we have to solve in implementing a FMM algorithm is organizing large amounts of data, also called data structuring. The non-adaptive FMM is appropriate when the particles are uniformly distributed while the adaptive FMM is most efficient when the distribution is non-uniform. In practice, we typically encounter highly non-uniform 3D particle distributions. This paper summarizes our implementation of a 3D adaptive FMM algorithm data structure setup for non-uniform particle distributions.

MOPPC094	Charge Density Estimations with Orthogonal Polynomials	355
	D. Hernandez, B. Erdelyi Northern Illinois University, DeKalb, Illinois, USA
	Funding: This work was supported by the Department of Energy under Contract No. DE-FG02-08ER41532 with Northern Illinois University. A beam’s charge density, treated as a smooth and continuous function can be approximated using orthogonal series, allowing a solution of Poisson’s equation to be found. Getting the most accurate solution to the electric potential requires the best approximated charge density. Several beam distributions are approximated using Jacobi polynomials generated by the recursion relation and the moment method. Varying both the particle number and order of the approximation gives a chance to not only compare the performance of the different polynomials, but allows to determine if a particular combination of order and particle number works better for a particular function. Although all three orthogonal polynomials used give similar results, the approximation coefficients should be allowed to converge and taken to high orders for best results. This is clearly seen on the single Gaussian approximation, where after five million particles, the difference between the distributions remains constant and the highest tested order gives best results.

TUEPPB007	A Self Consistent Multiprocessor Space Charge Algorithm that is Almost Embarrassingly Parallel	1128
	E.W. Nissen JLAB, Newport News, Virginia, USA B. Erdelyi Northern Illinois University, DeKalb, Illinois, USA S.L. Manikonda ANL, Argonne, USA
	Funding: Notice: Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. We present a space charge code that is self consistent, massively parallelizeable, and requires very little communication between the computer nodes; making the calculation almost embarrassingly parallel. This method is implemented in the code COSY Infinity where the differential algebras used in this code are important to the algorithm's proper functioning. The method works by calculating the self consistent charge distribution using the statistical moments of the test particles, and converting them into polynomial series coefficients. These coefficients are combined with differential algebraic integrals to form the potential, and electric fields. The result is a transfer map which contains the effects of space charge. This method allows for massive parallelization since its statistics based solver doesn’t require any binning of the particles, and only requires a vector containing the partial sums of the statistical moments for the different nodes to be passed. All other calculations are done independently. The resulting maps can be used to analyze the system using normal form analysis, as well as advance particles in numbers and at speeds that were previously impossible.

TUPPD011	Studies of the Twin Helix Parametric-resonance Ionization Cooling Channel with COSY INFINITY	1428
	J.A. Maloney, K.B. Beard, R.P. Johnson Muons, Inc, Batavia, USA A. Afanasev GWU, Washington, USA S.A. Bogacz, Y.S. Derbenev, V.S. Morozov JLAB, Newport News, Virginia, USA B. Erdelyi Northern Illinois University, DeKalb, Illinois, USA
	Funding: Supported in part by SBIR Grant DE-SC00005589. Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. A primary technical challenge to the design of a high luminosity muon collider is an effective beam cooling system. An epicyclic twin-helix channel utilizing parametric-resonance ionization cooling has been proposed for the final 6D cooling stage. A proposed design of this twin-helix channel is presented that utilizes correlated optics between the horizontal and vertical betatron periods to simultaneously focus transverse motion of the beam in both planes. Parametric resonance is induced in both planes via a system of helical quadrupole harmonics. Ionization cooling is achieved via periodically placed wedges of absorbing material, with intermittent rf cavities restoring longitudinal momentum necessary to maintain stable orbit of the beam. COSY INFINITY is utilized to simulate the theory at first order. The motion of particles around a hyperbolic fixed point is tracked. Comparison is made between the EPIC cooling channel and standard ionization cooling effects. Cooling effects are measured, after including stochastic effects, for both a single particle and a distribution of particles.

WEPPP005	Progress on Muon Parametric-resonance Ionization Cooling Channel Development	2729
	V.S. Morozov, Y.S. Derbenev JLAB, Newport News, Virginia, USA A. Afanasev GWU, Washington, USA K.B. Beard, R.P. Johnson Muons, Inc, Batavia, USA B. Erdelyi, J.A. Maloney Northern Illinois University, DeKalb, Illinois, USA
	Funding: Supported in part by DOE SBIR grant DE-SC0005589. Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. Parametric-resonance Ionization Cooling (PIC) is intended as the final 6D cooling stage of a high-luminosity muon collider. To implement PIC, a continuous-field twin-helix magnetic channel was developed. A 6D cooling with stochastic effects off is demonstrated in a GEANT4/G4beamline model of a system where wedge-shaped Be absorbers are placed at the appropriate dispersion points in the twin-helix channel and are followed by short rf cavities. To proceed to cooling simulations with stochastics on, compensation of the beam aberrations from one absorber to another is required. Initial results on aberration compensation using a set of various-order continuous multipole fields are presented. As another avenue to mitigate the aberration effect, we optimize the cooling channel’s period length. We observe a parasitic parametric resonance naturally occurring in the channel’s horizontal plane due to the periodic beam energy modulation caused by the absorbers and rf. We discuss options for compensating this resonance and/or properly combining it with the induced half-integer parametric resonance needed for PIC. The U.S. Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce this manuscript for U.S. Government purposes.

Paper

Title

Page

Formation of Beams in the Ion Accelerator Complex of the Medium Energy Electron Ion Collider Facility at JLab

88

S.L. Manikonda, P.N. Ostroumov
ANL, Argonne, USA
B. Erdelyi
Northern Illinois University, DeKalb, Illinois, USA

Funding: This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. DE-AC02-06CH11357.
At the interaction point of the Medium Energy Electron Ion Collider (MEIC) facility the luminosity of 10³³cm^-2s^-1 will be achieved through the collision of counter rotating beams of 0.5A ions and 3A electrons at 750MHz frequency. Formation of ion beams at MEIC is carried out in the Ion Accelerator Complex (IAC) comprising of a linac, pre-booster ring, booster ring, and a collider ring. We will describe the scheme proposed for the formation of ion beams at MEIC facility from the point of view of longitudinal beam dynamics. The proposed scheme minimizes losses due to space charge effects at low energies and needs moderate RF requirements already achieved at other existing facilities. Simulation studies have been conducted to verify the proposed scheme. We will present the results of these simulation studies.

MOPPC093

Optimal Fast Multipole Method Data Structures

352

S. Abeyratne, B. Erdelyi
Northern Illinois University, DeKalb, Illinois, USA
S.L. Manikonda
ANL, Argonne, USA

The Fast Multipole Method (FMM) has been identified as one of the ten most significant numerical algorithms discovered in the 20th century. The FMM guarantees finding fast solutions to many problems in science, such as calculating Coulomb potentials among large number of particles by reducing memory footprint and run time while attaining very high accuracy levels. One important practical issue that we have to solve in implementing a FMM algorithm is organizing large amounts of data, also called data structuring. The non-adaptive FMM is appropriate when the particles are uniformly distributed while the adaptive FMM is most efficient when the distribution is non-uniform. In practice, we typically encounter highly non-uniform 3D particle distributions. This paper summarizes our implementation of a 3D adaptive FMM algorithm data structure setup for non-uniform particle distributions.

MOPPC094

Charge Density Estimations with Orthogonal Polynomials

355

D. Hernandez, B. Erdelyi
Northern Illinois University, DeKalb, Illinois, USA

Funding: This work was supported by the Department of Energy under Contract No. DE-FG02-08ER41532 with Northern Illinois University.
A beam’s charge density, treated as a smooth and continuous function can be approximated using orthogonal series, allowing a solution of Poisson’s equation to be found. Getting the most accurate solution to the electric potential requires the best approximated charge density. Several beam distributions are approximated using Jacobi polynomials generated by the recursion relation and the moment method. Varying both the particle number and order of the approximation gives a chance to not only compare the performance of the different polynomials, but allows to determine if a particular combination of order and particle number works better for a particular function. Although all three orthogonal polynomials used give similar results, the approximation coefficients should be allowed to converge and taken to high orders for best results. This is clearly seen on the single Gaussian approximation, where after five million particles, the difference between the distributions remains constant and the highest tested order gives best results.

TUEPPB007

A Self Consistent Multiprocessor Space Charge Algorithm that is Almost Embarrassingly Parallel

1128

E.W. Nissen
JLAB, Newport News, Virginia, USA
B. Erdelyi
Northern Illinois University, DeKalb, Illinois, USA
S.L. Manikonda
ANL, Argonne, USA

Funding: Notice: Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177.
We present a space charge code that is self consistent, massively parallelizeable, and requires very little communication between the computer nodes; making the calculation almost embarrassingly parallel. This method is implemented in the code COSY Infinity where the differential algebras used in this code are important to the algorithm's proper functioning. The method works by calculating the self consistent charge distribution using the statistical moments of the test particles, and converting them into polynomial series coefficients. These coefficients are combined with differential algebraic integrals to form the potential, and electric fields. The result is a transfer map which contains the effects of space charge. This method allows for massive parallelization since its statistics based solver doesn’t require any binning of the particles, and only requires a vector containing the partial sums of the statistical moments for the different nodes to be passed. All other calculations are done independently. The resulting maps can be used to analyze the system using normal form analysis, as well as advance particles in numbers and at speeds that were previously impossible.

TUPPD011

Studies of the Twin Helix Parametric-resonance Ionization Cooling Channel with COSY INFINITY

1428

J.A. Maloney, K.B. Beard, R.P. Johnson
Muons, Inc, Batavia, USA
A. Afanasev
GWU, Washington, USA
S.A. Bogacz, Y.S. Derbenev, V.S. Morozov
JLAB, Newport News, Virginia, USA
B. Erdelyi
Northern Illinois University, DeKalb, Illinois, USA

Funding: Supported in part by SBIR Grant DE-SC00005589. Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177.
A primary technical challenge to the design of a high luminosity muon collider is an effective beam cooling system. An epicyclic twin-helix channel utilizing parametric-resonance ionization cooling has been proposed for the final 6D cooling stage. A proposed design of this twin-helix channel is presented that utilizes correlated optics between the horizontal and vertical betatron periods to simultaneously focus transverse motion of the beam in both planes. Parametric resonance is induced in both planes via a system of helical quadrupole harmonics. Ionization cooling is achieved via periodically placed wedges of absorbing material, with intermittent rf cavities restoring longitudinal momentum necessary to maintain stable orbit of the beam. COSY INFINITY is utilized to simulate the theory at first order. The motion of particles around a hyperbolic fixed point is tracked. Comparison is made between the EPIC cooling channel and standard ionization cooling effects. Cooling effects are measured, after including stochastic effects, for both a single particle and a distribution of particles.

WEPPP005

Progress on Muon Parametric-resonance Ionization Cooling Channel Development

2729

V.S. Morozov, Y.S. Derbenev
JLAB, Newport News, Virginia, USA
A. Afanasev
GWU, Washington, USA
K.B. Beard, R.P. Johnson
Muons, Inc, Batavia, USA
B. Erdelyi, J.A. Maloney
Northern Illinois University, DeKalb, Illinois, USA

Funding: Supported in part by DOE SBIR grant DE-SC0005589. Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177.
Parametric-resonance Ionization Cooling (PIC) is intended as the final 6D cooling stage of a high-luminosity muon collider. To implement PIC, a continuous-field twin-helix magnetic channel was developed. A 6D cooling with stochastic effects off is demonstrated in a GEANT4/G4beamline model of a system where wedge-shaped Be absorbers are placed at the appropriate dispersion points in the twin-helix channel and are followed by short rf cavities. To proceed to cooling simulations with stochastics on, compensation of the beam aberrations from one absorber to another is required. Initial results on aberration compensation using a set of various-order continuous multipole fields are presented. As another avenue to mitigate the aberration effect, we optimize the cooling channel’s period length. We observe a parasitic parametric resonance naturally occurring in the channel’s horizontal plane due to the periodic beam energy modulation caused by the absorbers and rf. We discuss options for compensating this resonance and/or properly combining it with the induced half-integer parametric resonance needed for PIC.
The U.S. Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce this manuscript for U.S. Government purposes.