Positron Capture Simulations: Runge-Kutta vs Boris

Slides:

Advertisements

Similar presentations

Wed 20 Sept 06Spin Tracking Meeting1 Positron Capture Simulations: Runge-Kutta vs Boris Leo Jenner, Daresbury Labs.

Advertisements

A Study of Mechanical and Magnetic Issues for a Prototype Positron Source Target The positron source for the International Linear Collider (ILC) comprises.

Chapter 6 Differential Equations

Find the equation of the tangent line. 1.Find the equation for the slopes of the tangent lines 2.Find the slope for the specific x. 3.Find the order pair.

Finite Volume II Philip Mocz. Goals Construct a robust, 2nd order FV method for the Euler equation (Navier-Stokes without the viscous term, compressible)

MAT 594CM S10Fundamentals of Spatial ComputingAngus Forbes Week 2 : Dynamics & Numerical Methods Goal : To write a simple physics simulation Topics: Intro.

Jan '09Positron Target Status1 Positron Target Prototype - Status Leo Jenner.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 32 Ordinary Differential Equations.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 31 Ordinary Differential Equations.

Harvard University - Boston University - University of Maryland Numerical Micromagnetics Xiaobo TanJohn S. Baras P. S. Krishnaprasad University of Maryland.

Mon Oct 27LC-ABD, Dundee1 Positron Target Prototype - Status Leo Jenner.

Mon 03 July 06Laserwire Mini-Workshop1 Using Laserwires to Measure Emittance at the ILC Leo Jenner, Daresbury Labs.

Numerical Solutions of Ordinary Differential Equations

Status of Undulator-based Positron Source Baseline Design Leo Jenner, but based largely on a talk given by Jim Clarke to Positron DESY-Zeuthen,

Calculus and Analytic Geometry II Cloud County Community College Spring, 2011 Instructor: Timothy L. Warkentin.

Scalar (Dot) Product. Scalar Product by Components.

Smoothed Particle Hydrodynamics (SPH) Fluid dynamics The fluid is represented by a particle system Some particle properties are determined by taking an.

Numerical Integration and Rigid Body Dynamics for Potential Field Planners David Johnson.

Computer Animation Algorithms and Techniques

Slope Fields. Quiz 1) Find the average value of the velocity function on the given interval: [ 3, 6 ] 2) Find the derivative of 3) 4) 5)

1 Options for low energy spin manipulation Ken Moffeit, SLAC 2009 Linear Collider Workshop of the Americas 29 September to 3 October 2009 K. Moffeit, D.

SPECIALIST MATHS Differential Equations Week 1. Differential Equations The solution to a differential equations is a function that obeys it. Types of.

Integration for physically based animation CSE 3541 Matt Boggus.

Developing An Educational Rigid Body Dynamics Physics Engine By Neal Milstein.

PHY 301: MATH AND NUM TECH Contents Chapter 10: Numerical Techniques I. Integration A.Intro B.Euler  Recall basic  Predictor-Corrector C. Runge-Kutta.

Today’s class Ordinary Differential Equations Runge-Kutta Methods

G. Penn UC Berkeley / LBNL CBP July, 2002 NuFact 02 Imperial College, London Boris Push with Spatial Stepping.

ILC Positron Production and Capturing Studies: Update Wei Gai, Wanming Liu and Kwang-Je Kim Posipol Workshop, Orsay, France May 23-25, 2007 Work performed.

LC-ABD: WP2.3 (robust spin polarisation) and WP5.1 (helical undulator). Helical Collaboration I.R. Bailey, P. Cooke, J.B. Dainton, L.J. Jenner, L.I. Malysheva.

Spin Tracking at the ILC Positron Source with PPS-Sim POSIPOL’11 V.Kovalenko POSIPOL’11 V. Kovalenko 1, G. Moortgat-Pick 1, S. Riemann 2, A. Ushakov 1.

ILC Positron Production and Capturing Studies: Update Wei Gai, Wanming Liu and Kwang-Je Kim ILC GDE Meeting DESY May 30 – Jun2, 2007 Work performed for.

1 Positron Source Configuration Masao KURIKI ILC AG meeting at KEK, 2006 Jan. Positron Source Configuration KURIKI Masao and John Sheppard  BCD Description.

Numerical Integration for physically based animation

Advanced Computer Graphics Rigid Body Simulation

Part 7 - Chapter 25.

5.4 Runge-Kutta 4 Method.

NC Accelerator Structures

Ordinary Differential Equations

When you see… Find the zeros You think….

Chapter 2 Objectives Describe motion in terms of changing velocity.

Class Notes 18: Numerical Methods (1/2)

Unit 6 – Fundamentals of Calculus Section 6

SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM (Term 101) Section 04 Read , 26-2, 27-1 CISE301_Topic8L4&5.

Class Notes 19: Numerical Methods (2/2)

Ch 8.6: Systems of First Order Equations

Section Euler’s Method

Chapter 2 Objectives Describe motion in terms of changing velocity.

Ordinary differential equaltions:

Part 7 - Chapter 25.

Finite Volume Method Philip Mocz.

Warm-Up 9/24/13 Look in your group’s folder for a set of distance vs. time graphs. For each graph, calculate the slope of the line. The slope represents.

ILC Baseline Design: Physics with Polarized Positrons

Section 11.3 Euler’s Method

ORBITAL Trajectories!!! Made by Karol Sanchez

Numerical Analysis Lecture 37.

Numerical Solutions of Ordinary Differential Equations

Numerical Analysis Lecture 38.

Impact of Time Integration Scheme on Supercell Development

Numerical solution of first-order ordinary differential equations

SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM (Term 101) Section 04 Read , 26-2, 27-1 CISE301_Topic8L6.

Section 9.4 – Solving Differential Equations Symbolically

SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM Read , 26-2, 27-1 CISE301_Topic8L3 KFUPM.

6.4 Runge-Kutta 4 Method.

Over or Under ? Routine.

Differential equations

Reading Between the Lines!

Update on MEIC Ion Polarization Work

Numerical solution of first-order ordinary differential equations 1. First order Runge-Kutta method (Euler’s method) Let’s start with the Taylor series.

CISE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM Read , 26-2, 27-1 CISE301_Topic8L6 KFUPM.

Presentation transcript:

Positron Capture Simulations: Runge-Kutta vs Boris Leo Jenner, Daresbury Labs Mon 08 Jan 07 ELC WS (DL)

Outline… Positron capture optics What is Astra? Spin tracking… T-BMT equation Runge-Kutta integration method Boris’ method Mon 08 Jan 07 ELC WS (DL)

ILC Positron Source Layout Original baseline layout of ILC with undulator at 150GeV position in main linac. Mon 08 Jan 07 ELC WS (DL)

Capture Optics Design V.S.Kashikhin z z Two coil magnet gives focussing solenoid field Mon 08 Jan 07 ELC WS (DL)

ASTRA Klaus Floettmann No spin tracking… Mon 08 Jan 07 ELC WS (DL)

T-BMT Equation Lorentz Factor Differential Equation… Gyromagnetic anomaly Mon 08 Jan 07 ELC WS (DL)

Runge-Kutta Integrator Scheme Andriy Ushakov Let an initial value problem be specified as follows. Then, the RK4 method for this problem is given by the following equation: where Thus, the next value (yn+1) is determined by the present value (yn) plus the product of the size of the interval (h) and an estimated slope. The slope is a weighted average of slopes: k1 is the slope at the beginning of the interval; k2 is the slope at the midpoint of the interval, using slope k1 to determine the value of y at the point tn + h/2 using Euler's method; k3 is again the slope at the midpoint, but now using the slope k2 to determine the y-value; k4 is the slope at the end of the interval, with its y-value determined using k3. Mon 08 Jan 07 ELC WS (DL)

Boris’ Numerical Integration Scheme Advance w by vector term b a half-step Advance w by M a full step Advance w by b a half-step Mon 08 Jan 07 ELC WS (DL)

R-K vs Boris Will try both! Boris: 2nd order, good at preserving conserving quantities, 1 calculation per step R-K: 4th order, 4 calculations per step (speed!) Will try both! Mon 08 Jan 07 ELC WS (DL)

Conclusions… …but doesn’t have spin tracking included… ASTRA can be used to simulate the motion of particles/bunches in the capture optics section …but doesn’t have spin tracking included… Spin tracking routine using Boris integrator 1st draft ready Spin tracking subroutine using Runge-Kutta integrator underway – cross-check Merlin cross-check (Andy Wolski) Mon 08 Jan 07 ELC WS (DL)