ICAP2012 - Classification: 05 Computer Modeling of High Current Effects

Paper

Title

Page

Simulation of Electron Cloud Instability

26

K. Ohmi
KEK, Ibaraki, Japan

We discuss coupled bunch and single bunch instabilities caused by electron cloud in positron and proton circular accelerator. We focus unstable mode spectrum which characterizes the instabilities.

Slides MOACC2 [3.432 MB]

MOSCC1

Beam Dynamics Study concerning SIS-100 Proton Operation including Space Charge Effects

34

S. Sorge
GSI, Darmstadt, Germany

The projected SIS-100 synchrotron at GSI will be used for operation with intense proton and heavy ion beams. In order to avoid the crossing of the transition energy during proton operation a complicated optics scheme is proposed to provide a transition energy above the extraction energy of E=29 GeV. For the purpose of optimizing the lattice, and to find a suitable working point, regime simulation scans of the dynamic aperture are performed based on MAD-X tracking. In the next step working point candidates will be used for particle tracking simulations in order to estimate beam loss due to space charge induced resonance crossing. For these studies different codes and space charge models are considered.

Slides MOSCC1 [0.643 MB]

MOSCC2

Simulation of Space Effects During Multiturn Injection into the GSI SIS18 Synchrotron

37

S. Appel
GSI, Darmstadt, Germany
O. Boine-Frankenheim
TEMF, TU Darmstadt, Darmstadt, Germany

The optimization of the Multiturn Injection (MTI) from the UNILAC into the SIS18 is crucial in order to reach the FAIR beam intensities required for heavy ions. In order to achieve the design intensities, the efficiency of the multiturn injection from the UNILAC has to be optimized for high beam currents. We developed a simulation model for the MTI including the closed orbit bump, lattice errors, the parameters of the injected UNILAC beam, the position of the septum and other aperture limiting components, and finally the space charge force and other high-intensity effects. The model is also used to estimate the required proton and heavy-ion beam emittances from the UNILAC and from the projected p-linac. For the accurate prediction of the MTI efficiency a careful validation of the simulation model is necessary. We will present first results of the comparison between experiments and simulation for low and high uranium beam currents.

Slides MOSCC2 [2.511 MB]

TUAAI3

Simulation of Transverse Coherent Effects in Intense Ion Bunches

O. Boine-Frankenheim
TEMF, TU Darmstadt, Darmstadt, Germany
V. Kornilov
GSI, Darmstadt, Germany

The transverse stability thresholds for intense ion bunches in the FAIR synchrotrons as well as in other injector rings are determined by the interplay of space charge and transverse impedances. Also below the stability threshold space charge causes a strong modification of the head-tail modes, with implications for the interpretation of beam signals from Schottky probes and BTF measurements. In order to predict stability thresholds and signals from stable bunches the simulations should be able to account for the 3D self-consistent space charge field. Furthermore the accurate matching of the longitudinal particle distribution to different rf bucket forms is important in order to correctly resolve the head-tail mode spectrum. Results obtained with the code PATRIC for the FAIR synchrotron will be presented. Some analytic solutions available for code validation are pointed out.

TUSCI1

The Fast Multipole Method in the Differential Algebra Framework for the Computation of 3D Space Charge Fields and Transfer Maps

H. Zhang, M. Berz
MSU, East Lansing, Michigan, USA

A new algorithm which combines the classical multiple level fast multipole algorithm with differential algebraic tools for three dimensional electrostatic field calculation of N-body systems is presented. The whole charged domain is hierarchically decomposed into boxes of varying sizes according to the local charge density. Each box has a near region, where the interaction is calculated directly, and its a region, where the interaction is represented by expansions in multipoles at infinity. The total field is the summation of the near region field and the far region field. This algorithm can treat any arbitrary charge distribution with an efficiency of O(N). Differential algebra simplifies the math especially for non-point charge macro particles, and allows the calculation of high order field derivatives, which is essential to generate the transfer map. Examples of applying the methods in beam dynamics simulations are given.

Slides TUSCI1 [3.302 MB]

TUSCC2

The Convergence and Accuracy of the Matrix Formalism Approximation

93

S.N. Andrianov
St. Petersburg State University, St. Petersburg, Russia

Funding: The work is supported by Federal Targeted Program "Scientific and Scientific-Pedagogical Personnel of the Innovative Russia in 2009-2013" (Governmental Contract no. p 793)
To the present time there has been developed a large number of different codes for the particles beam dynamics modeling. However, their precision, accuracy and reliability of the numerical results are not sufficiently guaranteed in the case of long-term evolution of particle beams in circular accelerators. Here we discuss convergence estimates of the matrix presentation for Lie series. We also consider some problems of the matrix formalism accuracy for constructing the evolution operator of the particle beam. In this article there is paid a special attention to problems of symplecticity and energy conservation for long time evolution of particle beams.

Slides TUSCC2 [1.475 MB]

TUSDI1

Modeling of Coherent Synchrotron Radiation Using a Direct Numerical Solution of Maxwell's Equations

107

A. Novokhatski
SLAC, Menlo Park, California, USA

Funding: Work supported by Department of Energy DE-AC02-76SF00515
We present and discuss the properties of coherent electromagnetic fields of a very short, ultra-relativistic bunch, which travels in a rectangular vacuum under the influence of a bending force of a magnet. The analysis is based on the results of a direct numerical solution of Maxwell’s equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields. We also discuss coherent edge radiation. We present a clear picture of the field using the electric field lines constructed from the numerical solutions. This approach should be useful in the study of existing and future concepts of particle accelerators and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned.

Slides TUSDI1 [10.584 MB]

WESAI2

Space Charge and Electron Cloud Simulations

130

G. Franchetti
GSI, Darmstadt, Germany
F. Zimmermann
CERN, Geneva, Switzerland

Funding: AccNet
Tracking of high intensity effects for few turns of a circular accelerator is at reach of present computational capabilities. The situation is very different when the prediction of beam behaviour is extended to hundred of thousands of turns, where special approaches for the control of computer artifact are necessary sometimes to the expense of a complete physical modeling. The identification of the key physical ingredients helps to the development of computer algorithms capable of treating the long term tracking. In this talk it is presented the actual state of simulations for long term tracking of high intensity bunches of the SIS100 addressing the self consistent treatment of beam loss. A more realistic modeling of the incoherent effect of electron cloud is addressed as well.

Slides WESAI2 [7.523 MB]

WEP16

Analytical Presentation of Space Charge Forces

173

S.N. Andrianov
St. Petersburg State University, St. Petersburg, Russia

Funding: The work is supported by Federal Targeted Programme "Scientific and Scientific-Pedagogical Personnel of the Innovative Russia in 2009-2013" (Governmental Contract no. p 793)
This paper presents an analytical description of the space charge forces generated by charged particle beams. The suggested approach is based on some set of models for particle distribution function. All necessary calculations have analytical and closed form for different models for beam density distributions. These model distributions can be used for approximation of real beam distributions. The corresponding solutions are included in a general scheme of beam dynamics presentation based on the matrix formalism for Lie algebraic tools. The corresponding computer software is based on corresponding symbolic codes and some parallel technologies. In particular, as computational tools we consider GPU graphic card NVIDIA. As an example, there is considered the problem of modeling the beam dynamics for microprobe focusing systems.

WESCI2

Numerical Calculation of Beam Coupling Impedances in the Frequency Domain using FIT

193

U. Niedermayer, O. Boine-Frankenheim
TEMF, TU Darmstadt, Darmstadt, Germany

The transverse impedance of kicker magnets is considered to be one of the main beam instability sources in the projected SIS-100 at FAIR and also in the SPS at CERN. The longitudinal impedance can contribute to the heat load, which is especially a concern in the cold sections of SIS-100 and LHC. In the high frequency range, commercially available time domain codes like CST Particle Studio® serve to calculate the impedance but they become inapplicable at medium and low frequencies which become more important for larger size synchrotrons. We present the ongoing work of developing a Finite Integration (FIT) solver in frequency domain which is based on the Parallel and Extensible Toolkit for Scientific computing (PETSc) framework in C++. Pre- and post-processing are done in MATLAB®. Infinite beam pipe boundary conditions are used. The code is applied to an inductive insert used to compensate the longitudinal space charge impedance in low energy machines. Another application focuses on the impedance contribution of a ferrite kicker with inductively coupled pulse forming network (PFN) and frequency dependent complex material permeability.

Slides WESCI2 [3.468 MB]

WESCI3

Electromagnetic Characterization of Materials for the CLIC Damping Rings

198

E. Koukovini-Platia, G. De Michele, G. Rumolo
CERN, Geneva, Switzerland
C. Zannini
EPFL, Lausanne, Switzerland

The performance of the Compact Linear Collider (CLIC) damping rings (DR) is likely to be limited by collective effects due to the unprecedented brilliance of the beams. Coating will be used in both electron (EDR) and positron damping rings (PDR) to suppress effects like electron cloud formation or ion instabilities. The impedance modeling of the chambers, necessary for the instabilities studies which will ensure safe operation under nominal conditions, must include the contribution from the coating materials applied for electron cloud mitigation and/or ultra-low vacuum pressure. This advocates for a correct characterization of this impedance in a high frequency range, which is still widely unexplored. The electrical conductivity of the materials in the frequency range of few GHz is determined with the waveguide method, based on a combination of experimental measurements of the complex transmission coefficient S21 and CST 3D electromagnetic (EM) simulations.

Slides WESCI3 [2.488 MB]

THP07

Some Computational Challenges in the Modeling of Accelerators and their Solutions in the Simulation Code Warp

233

J.-L. Vay, C. Benedetti
LBNL, Berkeley, California, USA
R.H. Cohen, A. Friedman, D.P. Grote
LLNL, Livermore, California, USA

Funding: Supported by US-DOE Contracts DE-AC02-05CH11231 and DE-AC52-07NA27344, and the SciDAC/ComPASS project. Used resources of NERSC, supported by US-DOE Contract DE-AC02-05CH11231.
The Particle-In-Cell Code-Framework Warp originated in the Heavy Ion Fusion program to guide the development of accelerators that can deliver beams suitable for implosion of inertial fusion capsules. The range of application of Warp has considerably widened far beyond the initial area and it is now applied to the study and design of existing and next-generation high-energy accelerators, including, for example, the study of laser wakefield acceleration and electron cloud effects. We present an overview of Warp's capabilities, summarizing recent original numerical methods that were developed to address computational challenges such as space and time scale disparities, spurious numerical dispersion, efficient wideband digital filtering on parallel platforms, etc. The original methods include simulations in Lorentz boosted frames, an electromagnetic solver with tunable numerical dispersion and efficient stride-based digital filtering, Particle-In-Cell with Adaptive Mesh Refinement, a large-timestep ‘‘drift-Lorentz'' mover for arbitrarily magnetized species, and a relativistic Lorentz invariant leapfrog particle pusher. Selected examples of applications will be given.

THSDI2

Simulation of Multibunch Instabilities with the HEADTAIL Code

262

N. Mounet, E. Métral, G. Rumolo
CERN, Geneva, Switzerland

Multibunch instabilities due to beam-coupling impedance can be a critical limitation for synchrotrons operating with many bunches. To study these instabilities, the HEADTAIL code has been extended to simulate the motion of many bunches under the action of wake fields. All the features already present in the single-bunch version of the code have remained available, in particular synchrotron motion, chromaticity, amplitude detuning due to octupoles and the ability to load any kind of wake fields through tables. The code has been then parallelized in order to track thousands of bunches in a reasonable amount of time, showing a linear scaling with the number of processors used. We show benchmarks against Laclare's theory in simple cases, obtaining a good agreement. Results for bunch trains in the LHC and comparison with beam-based measurements are also exhibited.

Slides THSDI2 [7.278 MB]

THSDC3

Calculation of Longitudinal Instability Threshold Currents for Single Bunches

267

P. Kuske
HZB, Berlin, Germany

Based on the publication by M. Venturini, et al.[1] a computer program has been written that solves the Vlasov-Fokker-Planck equation numerically on a two dimensional grid. In this code different types of longitudinal interactions and their combinations are implemented like the shielded CSR- as well as the purely resistive and inductive interactions of the electrons within the bunch. The details of the program will be presented in the paper. Calculations have been performed for the 1.7 GeV storage ring BESSY II and the 600 MeV ring MLS. The results are compared with measurements on both rings which were based on the observation of the onset of bursts of coherent synchrotron radiation. Fair agreement is found between theoretical and experimental observations. The theoretical results complement calculations performed by Bane, et al. for the shielded CSR-interaction [2]. The new results emphasize the resistive nature of the CSR-Interaction, especially in regions where shielding effects are small.
[1] M. Venturini, et al., Phys. Rev. ST-SB, 8, 014202(2005)
[2] K.L.F. Bane, et al., “Comparison of Simulation Codes for Microwave Instability in Bunched Beams“, IPAC 2010, Kyoto, Japan

Slides THSDC3 [1.006 MB]

Paper	Title	Page
MOACC2	Simulation of Electron Cloud Instability	26
	K. Ohmi KEK, Ibaraki, Japan
	We discuss coupled bunch and single bunch instabilities caused by electron cloud in positron and proton circular accelerator. We focus unstable mode spectrum which characterizes the instabilities.
	Slides MOACC2 [3.432 MB]

MOSCC1	Beam Dynamics Study concerning SIS-100 Proton Operation including Space Charge Effects	34
	S. Sorge GSI, Darmstadt, Germany
	The projected SIS-100 synchrotron at GSI will be used for operation with intense proton and heavy ion beams. In order to avoid the crossing of the transition energy during proton operation a complicated optics scheme is proposed to provide a transition energy above the extraction energy of E=29 GeV. For the purpose of optimizing the lattice, and to find a suitable working point, regime simulation scans of the dynamic aperture are performed based on MAD-X tracking. In the next step working point candidates will be used for particle tracking simulations in order to estimate beam loss due to space charge induced resonance crossing. For these studies different codes and space charge models are considered.
	Slides MOSCC1 [0.643 MB]

MOSCC2	Simulation of Space Effects During Multiturn Injection into the GSI SIS18 Synchrotron	37
	S. Appel GSI, Darmstadt, Germany O. Boine-Frankenheim TEMF, TU Darmstadt, Darmstadt, Germany
	The optimization of the Multiturn Injection (MTI) from the UNILAC into the SIS18 is crucial in order to reach the FAIR beam intensities required for heavy ions. In order to achieve the design intensities, the efficiency of the multiturn injection from the UNILAC has to be optimized for high beam currents. We developed a simulation model for the MTI including the closed orbit bump, lattice errors, the parameters of the injected UNILAC beam, the position of the septum and other aperture limiting components, and finally the space charge force and other high-intensity effects. The model is also used to estimate the required proton and heavy-ion beam emittances from the UNILAC and from the projected p-linac. For the accurate prediction of the MTI efficiency a careful validation of the simulation model is necessary. We will present first results of the comparison between experiments and simulation for low and high uranium beam currents.
	Slides MOSCC2 [2.511 MB]

TUAAI3	Simulation of Transverse Coherent Effects in Intense Ion Bunches
	O. Boine-Frankenheim TEMF, TU Darmstadt, Darmstadt, Germany V. Kornilov GSI, Darmstadt, Germany
	The transverse stability thresholds for intense ion bunches in the FAIR synchrotrons as well as in other injector rings are determined by the interplay of space charge and transverse impedances. Also below the stability threshold space charge causes a strong modification of the head-tail modes, with implications for the interpretation of beam signals from Schottky probes and BTF measurements. In order to predict stability thresholds and signals from stable bunches the simulations should be able to account for the 3D self-consistent space charge field. Furthermore the accurate matching of the longitudinal particle distribution to different rf bucket forms is important in order to correctly resolve the head-tail mode spectrum. Results obtained with the code PATRIC for the FAIR synchrotron will be presented. Some analytic solutions available for code validation are pointed out.

TUSCI1	The Fast Multipole Method in the Differential Algebra Framework for the Computation of 3D Space Charge Fields and Transfer Maps
	H. Zhang, M. Berz MSU, East Lansing, Michigan, USA
	A new algorithm which combines the classical multiple level fast multipole algorithm with differential algebraic tools for three dimensional electrostatic field calculation of N-body systems is presented. The whole charged domain is hierarchically decomposed into boxes of varying sizes according to the local charge density. Each box has a near region, where the interaction is calculated directly, and its a region, where the interaction is represented by expansions in multipoles at infinity. The total field is the summation of the near region field and the far region field. This algorithm can treat any arbitrary charge distribution with an efficiency of O(N). Differential algebra simplifies the math especially for non-point charge macro particles, and allows the calculation of high order field derivatives, which is essential to generate the transfer map. Examples of applying the methods in beam dynamics simulations are given.
	Slides TUSCI1 [3.302 MB]

TUSCC2	The Convergence and Accuracy of the Matrix Formalism Approximation	93
	S.N. Andrianov St. Petersburg State University, St. Petersburg, Russia
	Funding: The work is supported by Federal Targeted Program "Scientific and Scientific-Pedagogical Personnel of the Innovative Russia in 2009-2013" (Governmental Contract no. p 793) To the present time there has been developed a large number of different codes for the particles beam dynamics modeling. However, their precision, accuracy and reliability of the numerical results are not sufficiently guaranteed in the case of long-term evolution of particle beams in circular accelerators. Here we discuss convergence estimates of the matrix presentation for Lie series. We also consider some problems of the matrix formalism accuracy for constructing the evolution operator of the particle beam. In this article there is paid a special attention to problems of symplecticity and energy conservation for long time evolution of particle beams.
	Slides TUSCC2 [1.475 MB]

TUSDI1	Modeling of Coherent Synchrotron Radiation Using a Direct Numerical Solution of Maxwell's Equations	107
	A. Novokhatski SLAC, Menlo Park, California, USA
	Funding: Work supported by Department of Energy DE-AC02-76SF00515 We present and discuss the properties of coherent electromagnetic fields of a very short, ultra-relativistic bunch, which travels in a rectangular vacuum under the influence of a bending force of a magnet. The analysis is based on the results of a direct numerical solution of Maxwell’s equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields. We also discuss coherent edge radiation. We present a clear picture of the field using the electric field lines constructed from the numerical solutions. This approach should be useful in the study of existing and future concepts of particle accelerators and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned.
	Slides TUSDI1 [10.584 MB]

WESAI2	Space Charge and Electron Cloud Simulations	130
	G. Franchetti GSI, Darmstadt, Germany F. Zimmermann CERN, Geneva, Switzerland
	Funding: AccNet Tracking of high intensity effects for few turns of a circular accelerator is at reach of present computational capabilities. The situation is very different when the prediction of beam behaviour is extended to hundred of thousands of turns, where special approaches for the control of computer artifact are necessary sometimes to the expense of a complete physical modeling. The identification of the key physical ingredients helps to the development of computer algorithms capable of treating the long term tracking. In this talk it is presented the actual state of simulations for long term tracking of high intensity bunches of the SIS100 addressing the self consistent treatment of beam loss. A more realistic modeling of the incoherent effect of electron cloud is addressed as well.
	Slides WESAI2 [7.523 MB]

WEP16	Analytical Presentation of Space Charge Forces	173
	S.N. Andrianov St. Petersburg State University, St. Petersburg, Russia
	Funding: The work is supported by Federal Targeted Programme "Scientific and Scientific-Pedagogical Personnel of the Innovative Russia in 2009-2013" (Governmental Contract no. p 793) This paper presents an analytical description of the space charge forces generated by charged particle beams. The suggested approach is based on some set of models for particle distribution function. All necessary calculations have analytical and closed form for different models for beam density distributions. These model distributions can be used for approximation of real beam distributions. The corresponding solutions are included in a general scheme of beam dynamics presentation based on the matrix formalism for Lie algebraic tools. The corresponding computer software is based on corresponding symbolic codes and some parallel technologies. In particular, as computational tools we consider GPU graphic card NVIDIA. As an example, there is considered the problem of modeling the beam dynamics for microprobe focusing systems.

WESCI2	Numerical Calculation of Beam Coupling Impedances in the Frequency Domain using FIT	193
	U. Niedermayer, O. Boine-Frankenheim TEMF, TU Darmstadt, Darmstadt, Germany
	The transverse impedance of kicker magnets is considered to be one of the main beam instability sources in the projected SIS-100 at FAIR and also in the SPS at CERN. The longitudinal impedance can contribute to the heat load, which is especially a concern in the cold sections of SIS-100 and LHC. In the high frequency range, commercially available time domain codes like CST Particle Studio® serve to calculate the impedance but they become inapplicable at medium and low frequencies which become more important for larger size synchrotrons. We present the ongoing work of developing a Finite Integration (FIT) solver in frequency domain which is based on the Parallel and Extensible Toolkit for Scientific computing (PETSc) framework in C++. Pre- and post-processing are done in MATLAB®. Infinite beam pipe boundary conditions are used. The code is applied to an inductive insert used to compensate the longitudinal space charge impedance in low energy machines. Another application focuses on the impedance contribution of a ferrite kicker with inductively coupled pulse forming network (PFN) and frequency dependent complex material permeability.
	Slides WESCI2 [3.468 MB]

WESCI3	Electromagnetic Characterization of Materials for the CLIC Damping Rings	198
	E. Koukovini-Platia, G. De Michele, G. Rumolo CERN, Geneva, Switzerland C. Zannini EPFL, Lausanne, Switzerland
	The performance of the Compact Linear Collider (CLIC) damping rings (DR) is likely to be limited by collective effects due to the unprecedented brilliance of the beams. Coating will be used in both electron (EDR) and positron damping rings (PDR) to suppress effects like electron cloud formation or ion instabilities. The impedance modeling of the chambers, necessary for the instabilities studies which will ensure safe operation under nominal conditions, must include the contribution from the coating materials applied for electron cloud mitigation and/or ultra-low vacuum pressure. This advocates for a correct characterization of this impedance in a high frequency range, which is still widely unexplored. The electrical conductivity of the materials in the frequency range of few GHz is determined with the waveguide method, based on a combination of experimental measurements of the complex transmission coefficient S21 and CST 3D electromagnetic (EM) simulations.
	Slides WESCI3 [2.488 MB]

THP07	Some Computational Challenges in the Modeling of Accelerators and their Solutions in the Simulation Code Warp	233
	J.-L. Vay, C. Benedetti LBNL, Berkeley, California, USA R.H. Cohen, A. Friedman, D.P. Grote LLNL, Livermore, California, USA
	Funding: Supported by US-DOE Contracts DE-AC02-05CH11231 and DE-AC52-07NA27344, and the SciDAC/ComPASS project. Used resources of NERSC, supported by US-DOE Contract DE-AC02-05CH11231. The Particle-In-Cell Code-Framework Warp originated in the Heavy Ion Fusion program to guide the development of accelerators that can deliver beams suitable for implosion of inertial fusion capsules. The range of application of Warp has considerably widened far beyond the initial area and it is now applied to the study and design of existing and next-generation high-energy accelerators, including, for example, the study of laser wakefield acceleration and electron cloud effects. We present an overview of Warp's capabilities, summarizing recent original numerical methods that were developed to address computational challenges such as space and time scale disparities, spurious numerical dispersion, efficient wideband digital filtering on parallel platforms, etc. The original methods include simulations in Lorentz boosted frames, an electromagnetic solver with tunable numerical dispersion and efficient stride-based digital filtering, Particle-In-Cell with Adaptive Mesh Refinement, a large-timestep ‘‘drift-Lorentz'' mover for arbitrarily magnetized species, and a relativistic Lorentz invariant leapfrog particle pusher. Selected examples of applications will be given.

THSDI2	Simulation of Multibunch Instabilities with the HEADTAIL Code	262
	N. Mounet, E. Métral, G. Rumolo CERN, Geneva, Switzerland
	Multibunch instabilities due to beam-coupling impedance can be a critical limitation for synchrotrons operating with many bunches. To study these instabilities, the HEADTAIL code has been extended to simulate the motion of many bunches under the action of wake fields. All the features already present in the single-bunch version of the code have remained available, in particular synchrotron motion, chromaticity, amplitude detuning due to octupoles and the ability to load any kind of wake fields through tables. The code has been then parallelized in order to track thousands of bunches in a reasonable amount of time, showing a linear scaling with the number of processors used. We show benchmarks against Laclare's theory in simple cases, obtaining a good agreement. Results for bunch trains in the LHC and comparison with beam-based measurements are also exhibited.
	Slides THSDI2 [7.278 MB]

THSDC3	Calculation of Longitudinal Instability Threshold Currents for Single Bunches	267
	P. Kuske HZB, Berlin, Germany
	Based on the publication by M. Venturini, et al.[1] a computer program has been written that solves the Vlasov-Fokker-Planck equation numerically on a two dimensional grid. In this code different types of longitudinal interactions and their combinations are implemented like the shielded CSR- as well as the purely resistive and inductive interactions of the electrons within the bunch. The details of the program will be presented in the paper. Calculations have been performed for the 1.7 GeV storage ring BESSY II and the 600 MeV ring MLS. The results are compared with measurements on both rings which were based on the observation of the onset of bursts of coherent synchrotron radiation. Fair agreement is found between theoretical and experimental observations. The theoretical results complement calculations performed by Bane, et al. for the shielded CSR-interaction [2]. The new results emphasize the resistive nature of the CSR-Interaction, especially in regions where shielding effects are small. [1] M. Venturini, et al., Phys. Rev. ST-SB, 8, 014202(2005) [2] K.L.F. Bane, et al., “Comparison of Simulation Codes for Microwave Instability in Bunched Beams“, IPAC 2010, Kyoto, Japan
	Slides THSDC3 [1.006 MB]