BEND MAGNET HEAT LOADS & OUT OF ORBIT SCENARIOS d r h g f d - PowerPoint PPT Presentation

BEND MAGNET HEAT LOADS & OUT OF ORBIT SCENARIOS d r h g f d j h n g n g f m h g m g h m g h j m g h f m f TIM VALICENTI Lee Teng Intern Wednesday, August 3 rd Lemont, Illinois

OVERVIEW

THE PROBLEM This is an optimization problem… • What power distributions do the APS-U bend magnets emit? • Changing the position and orientation of absorbing surfaces can reduce the peak intensity. • Important for the design of components under thermal stress Y X Z 3

TASKS 1. Find ideal path 2. Include orbit errors 3. Ray trace photons 4. Calculate heat loads 5. Verify results (SynRad) 4

PROCESS Lattice files Ideal Particle from Elegant Trajectory Missteering Ray Tracing (Orbital Errors) Power Optimization Distributions 5

THEORY

IDEAL PATH Uses the parameterization of an arc of a circle along with a rotation matrix and a translation vector… 𝑨(𝑢) 𝑨(𝑢) 𝑨(𝑢) 𝜍 sin 𝜕𝑢 𝜍 sin 𝜕𝑢 𝜍 sin 𝜕𝑢 𝑦(𝑢) = 3(𝜄) 3(𝜄) 𝑦(𝑢) 𝑦(𝑢) 𝜍 cos 𝜕𝑢 − 1 = 𝑆 = 𝑆 + 𝑠̅ 8 𝜍 cos 𝜕𝑢 − 1 𝜍 cos 𝜕𝑢 − 1 𝑧(𝑢) 𝑧(𝑢) 𝑧(𝑢) 0 0 0 7

IDEAL PATH - VARIABLES § Δϴ = θ 0 – θ 1 : dipole kick. θ 1 is used in the rotation matrix ∆; § 𝐶 = 𝑴𝒇𝒐𝒉𝒖𝒊 𝐶𝜍 : uses the rigidity, length, and kick to get the B-field 𝒕𝑭𝒐𝒆 𝟏 M𝒕𝑻𝒖𝒃𝒔𝒖 𝟏 § 𝑢 = 0.. 𝑢 D 𝑥ℎ𝑓𝑠𝑓 𝑢 D = : the time for which the bunch travels Q 𝒂 𝟐 , 𝒀 𝟐 , 𝒕𝑭𝒐𝒆 𝟐 RS T Q § 𝜍 = U T V : the radius of curvature 𝜄 k ? , ? , 𝐭𝐓𝐮𝐛𝐬𝐮 𝟏 W 𝜀𝑡 = 𝑡𝑇𝑢𝑏𝑠𝑢 8 − 𝑡𝐹𝑜𝑒 k § 𝜕 = Q : effective frequency 𝑎 8 § 𝑠 8 = 𝑌 8 : the initial position 𝑎 8 = 𝑎 k + 𝜀𝑡 ∗ cos (𝜄 k ) 0 𝑌 8 = 𝑌 k + 𝜀𝑡 ∗ sin (𝜄 k ) 8

MISSTEERING Bolded values come from the lattice files; everything else is either a constant of the accelerator or are already calculated. 𝒝 n = 𝛿 p 𝑦 q + 𝜷 𝒚 𝑦𝑦 t + 𝜸 𝒚 𝑦 tq 𝒝 n = 𝛿 v 𝑧 q + 𝜷 𝒛 𝑧𝑧 + 𝜸 𝒛 𝑧 tq 9

VISUALIZATION OF LOCAL COORDINATES The global and local y-coordinates are equal while the x-coordinates differ. x’ is equivalent to dx/ds while y’ is the vertical analog: dy/ds. y x s Y X Z x’ x y y’ s s 10

RAY TRACING One can use their knowledge of the absorbing plane as well as the location of the electron bunch to accurately calculate rays. Consider the velocity vector at time step: t = 𝑢 t • 𝑡 | 𝑎(𝑒) 𝑡 } 𝑌(𝑒) The equation for the ray leaving that point is: P d = = 𝑒 + 𝑠 𝑢′ • 𝑡 ~ 𝑍(𝑒) The equation for the plane is: 𝑜 € • 𝑄(𝑎, 𝑌,𝑍) − 𝑄 8 = 0 • Substitute 𝑄 𝑎,𝑌, 𝑍 = 𝑄(𝑒) and solve for 𝑒 to find the point on the plane • where the ray lands. x y 𝑜 € s Y X Z 11

POWER DISTRIBUTION One must consider both the horizontal and vertical spread of power • Finding vertical spread on the absorber may be difficult but once done one can find the angles each vertical ray makes with the zero-angle ray. Use: ƒ „ … } „ k‡} „ ˆ/„ 1 + Š k • ƒ;ƒ† = 𝑄 8 k‡} „ , 𝑌 = 𝛿𝜄 ‹ = 5.421 ∗ 𝐹 ” 𝐻𝑓𝑊 ∗ 𝐽 𝐵 ∗ 𝐶(𝑈) o where 𝑄 Œ ⁄ 8 S•Ž • „ • If the vertical rays are known, their distances, D, can be calculated and the k intensity at each point on the plane can be converted as š „ P Œ → 𝑄 Œ ⁄ ⁄ S•Ž• „ SS „ x y s 𝜄 Y X Z 12

RESULTS

MISSTEERING User can enter which missteered paths they want to consider (alternatively the code has a default set of missteered paths). Note the y-axis scale. y x X 14

EXAMPLE Shows the rays from 4 consecutive bend magnets – M3.1, M3.2, M2.5, M2.4 – hitting the B-crotch absorber. M3.1 M3.2 M2.5 M2.4 15

EXAMPLE Shows the rays from 4 consecutive bend magnets – M3.1, M3.2, M2.5, M2.4 – hitting the B-crotch absorber. M3.1 M3.2 M2.5 M2.4 16

EXAMPLE Shows the intensity from 4 consecutive bend magnets – M3.1, M3.2, M2.5, M2.4 – hitting the B-crotch absorber. 17

VALIDATION WITH SYNRAD The data matches very well 250 SynRad: 2.84 kW 200 This software: 2.84 kW 150 100 50 0 0 10 20 30 40 50 60 70 80 90 18

ADVANTAGES AND APPLICATIONS • ANALYTICAL FUNCTIONS ALLOW EASY INTEGRATION WITH OTHER PROGRAMS SUCH AS COMSOL • STARTING WITH THE LATTICE FILES ONE GAINS FULL BUNCH TRAJECTORIES BOTH IDEAL AND WITH ERROR • CAN USE ANY OF THESE TRAJECTORIES TO DETERMINE THE POWER DISTRIBUTION. • CAN EASILY OPTIMIZE BY CHANGING POSITION AND NORMAL VECTOR OF THE ABSORBING PLANE.

ACHIEVEMENTS / FUTURE WORK • Calculated ideal paths via lattice files • Found missteered paths in 3 dimensions • Accurately ray traced arbitrary trajectories • Solved for the heat map on any given planar surface • Verified results with SynRad • A more friendly UI (perhaps a GUI) • COMSOL Integration • More geometries of absorbers • Insertion device analogs

SUMMER EXPERIENCE • ATTENDED USPAS TO TAKE A FULL COURSE ON ACCELERATOR PHYSICS • LEARNED MORE THAN MOST ADVANCED E&M BOOKS COVER • GAINED INVALUABLE EXPERIENCE IN BOTH MATLAB AND COMSOL • HAD THE CHANCE TO MAKE AN IMPACT AT A PLACE LIKE ARGONNE WHILE STILL A STUDENT • HIKED A MOUNTAIN

ACKNOWLEDGEMENTS A VERY SPECIAL THANKS TO KAMLESH SUTHAR FOR HIS GUIDANCE ON THIS PROJECT; TO JASON CARTER, JASON LERCH, KATHY HARKAY, AND ROGER DEJUS FOR THEIR INSIGHT ALONG THE WAY; AND ESPECIALLY TO PAT DEN HARTOG, ERIC PREBYS, AND LINDA SPENTZOURIS FOR GIVING ME THIS OPPORTUNITY AND ORGANIZING THE SUMMER 2016 STUDENT INTERNSHIPS. www.anl.gov

CITATIONS • CAPATINA, DANA. PRIVATE COMMUNICATION (2016). • CARTER, JASON. PRIVATE COMMUNICATION (2016). • CHAO, ALEXANDER WU., AND M. TIGNER. HANDBOOK OF ACCELERATOR PHYSICS AND ENGINEERING . RIVER EDGE, NJ: WORLD SCIENTIFIC, 1999. PRINT. • DEJUS, ROGER. "POWER DISTRIBUTION FROM A DIPOLE SOURCE." INTERNAL APS MEMO (2003): 1-8. PRINT. • EDWARDS, D. A., AND M. J. SYPHERS. AN INTRODUCTION TO THE PHYSICS OF HIGH ENERGY ACCELERATORS . NEW YORK: WILEY, 1993. PRINT. • HARKAY, KATHERINE. "MAXIMUM BEAM ORBIT IN MBA AND RAY TRACING GUIDELINES." 2ND SER. (2014): 1-9. PRINT. • SUTHAR, KAMLESH. PRIVATE COMMUNICATION (2016). www.anl.gov