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UNIVERSIDADE PRESBITERIANA MACKENZIE

ESCOLA DE ENGENHARIA

CRAAM - CENTRO DE RÁDIO ASTRONOMIA E ASTROFÍSICA MACKENZIE

Rua da Consolação, 896 - CEP 01302-907 Fone: 2114-8734 - Fax: 3255-3123 - SÃO PAULO

Internet: www.craam.mackenzie.br

São Paulo, 19 de dezembro de 2011. Ao

Mackpesquisa

Ref.: Relatório das visitas dos pesquisadores Dr. John Michael Klopf e Dr. Balsa Terzic

Dr. John Michael Klopf e Dr.Balsa Terzic, pesquisadores do Jefferson Laboratory, EUA, chegaram ao Brasil dia 11/12/2011 com o objetivo de continuar as discussões a respeito de artigos a serem publicados com resultados das pesquisas referentes aos aceleradores e suas simulações aplicadas a explosões solares

Como divulgação de resultados apresentados até o momento, o pesquisador Dr. Balsa Terzic apresentou dia 12/12/2011 a palestra “New particle-in-cell code for umerical simulation of coherent synchrotron radiation” para os professores, alunos e convidados. O Dr. John Michael Klopf apresentou os resultados com outra palestra no dia 15/12/2011 “Examination of broadband coherent synchrotron radiation to describe THz and Sub-THz solar flare spectral simulation”, também para os professores, alunos e convidados.

A visita dos dois pesquisadores foi muito proveitosa, pois além as discussões já abertas outras ideias foram melhor trabalhadas com resultados interessantes para publicações de outros papers a serem submetidos a periódicos arbitrados.

Pierre Kaufmann Pesquisador líder Anexos:

- cartazes de divulgação das apresentações - apresentações

Dr. J. Michael Klopf

Outline

•  Jefferson Lab – Newport News, VA, USA

•  JLab high power THz and FEL sources

•  Applications and studies using the JLab THz and FEL sources

•  THz – accelerator studies, testing of prototype

instrumentation, dynamics, material under extremes

•  FEL – RIR PLD, photo-induced transformations,

time-resolved photoemission

•  Description of CSR process in laboratory accelerators

•  How do we connect CSR in lab accelerators to flare accelerators

•  Results from basic CSR simulations to fit anomalous

double-peaked flare spectral observations

•  How we can improve and expand our study of possible

Jefferson Lab – THz Source

M1

200x200mm 60x60mm

F2

200x200mm

M2

200x200mm

M4

F3

60x60mm THz To User Facility

Optical calculations by Oleg Chubar, Paul Dumas

Funding US Army NVL

CSR (THz) and FEL (IR) Spectral Flux

JLab THz Synchrotrons JLab FEL Table-top sub-ps lasers

FEL proof of principle: Neil et al. Phys. Rev.Letts

84, 662 (2000).

THz proof of principle:

Carr, Martin, McKinney, Neil, Jordan & Williams Nature 420, 153 (2002).

CSR (THz) and FEL (IR/UV/VUV) Spectral Flux

Av er ag e   B ri gh tn es s   (p ho to ns /s ec /mm 2 /mr ad 2 )   2nd  _Generation   3rd  _Generation   4th  _Generation   JLab  FEL    potential     upgrade  path  

Applications of the JLab THz source

•  Frequency and energy range of the THz spectrum overlaps numerous

material properties of interest

•  plasma oscillations

(charge density, mobility, effective mass)

•  phonon resonances

(lattice structure, strain)

•  superconducting band gaps

(DOS, e-p interactions)

•  free carrier absorption

(free carrier concentration)

•  surface plasmon resonances

(surface and interface phenomena)

•  Ultrashort pulsewidth enables sub-ps time resolution

•  pump-probe studies

(non-equilibrium relaxation and thermalization)

•  high E field studies

(single- to half-cycle pulses)

•  Novel radial polarization may be useful (radially oriented E field)

•  16 T magnet – magneto-optical studies

Applications of the JLab THz source

•  Prototype single-shot Holographic

Fourier Transform Spectrometer

•  Ultrashort pulsewidth of THz

pulses [

τ

_p

O

(100 fs)] enables sub-ps

time resolution

•  accelerator diagnostics

(bunch-to-bunch performance/stability)

•  single-shot measurements

(observation of dynamic states in

matter)

•  non-reversible transformations

(observe transformation as they

Probing of Materials Under Extreme Conditions

DAC with 100 µm aperture DTGS pyroelectric sensor

(collaboration with Carnegie Institution in Washington-Geophysical Laboratory)

T

H

z be

Applications of the JLab THz source

•  THz/MIR

double-resonance

•  gas phase

experiment

•  measure

energy x-fer

from

rotational to

vibrational

modes

(direct or

indirect

process?)

Applications of the JLab FEL sources

•  IR FEL

•  RIR PLD

(tunability enables targeting of resonances to avoid bond

breaking during ablation of polymers for thin film organics – R.

Haglund, Vanderbilt University)

•  photolysis of biological tissue

(selective destruction of lipid cells with

no collateral damage to surrounding healthy tissue – R. Anderson,

Harvard Medical)

•  photon-induced proton transport

(resonant photoexcitation of H

defects to increase mobilty – G. Luepke, William & Mary University)

•  UV/VUV FEL

•  phototransformation for laser micromachining

(micromachining of

3D structures, machining of subsurface structures – H. Helvajian,

Aerospace Corp.)

•  time-resolved photoemission based experiments

(combustion

dynamics – C. Taatjes, Sandia; Kr dating – Z.-T. Lu, Argonne;

ARPES – P. Johnson, Brookhaven)

Applications of the JLab FEL sources

Laser Input

Step motor for substrate holder and rotation

Valve

sample load chamber

Chamber

Transport arm

Liquid organic feeder Pressure gauges Target holder Substrate holder Substrate heater Pressure gauge Liquid N₂ bath

•  PLD system interfaced to JLab FEL and

table-top lasers

Coherent Synchrotron Radiation From Short Electron Bunches

•  acceleration of e- bunches off crest produces a monotonic energy spread or chirp

•  chicane provides dispersion and path geometry to

compress the chirped pulses _{long chirped pulse}

compressed pulse

Jefferson Lab – THz CSR Source Physics

E

le

ct

ri

c fi

el

d

time

freq. (1/time)

super-radiant enhancement N

E/N

Int

ens

it

y

⏐

E

2

⏐

electron(s)

Considering Short e- _Bunches incoherent synchrotron radiation from N e-_’s N

Connecting CSR from the Lab to a Solar Flare

•  1985 - Pierre et al. published first observations of new high

frequency spectral component at 90 GHz

P. Kaufmann, E. Correia, J. E. R. Costa, A. M. Zodi Vaz and B. R. Dennis, Solar burst with

millimetre-wave emission at high frequency only, Nature, 313, 380-382, (1985).

•  ~ 11/2006 - Pierre initiated contact with Gwyn Williams and M.

Klopf regarding published CSR measurements from the JLab

FEL accelerator

G. L. Carr, M. C. Martin, W. R. McKinney, K. Jordan, G. R. Neil and G. P. Williams, High-power

terahertz radiation from relativistic electrons, Nature, 420, 153-156, (2002).

•  Discussions led to a collaborative effort to investigate the

possibility of CSR processes in solar flare structures

•  2008 - presented first attempts to correlate double-peaked

spectral component to CSR emission

(SMESE Workshop)

•  2010 - presented first CSR simulations to fit flare

Connecting CSR from the Lab to a Solar Flare

•  The concept of coherent enhancement at wavelengths long

relative to the electron bunch dimensions was proposed quite

long ago[1], but was not examined experimentally until the

1980’s[2].

•  Around the same time, this coherent emission mechanism was

presented as a possible radiation process in the radio emission of

pulsars[3].

•  Soon after, the theory of coherent synchrotron radiation (CSR)

was formally developed[4] and has been fully demonstrated

more recently[5].

1.  L. I. Schiff, Production of Particle Energies beyond 200 Mev, Rev. Sci. Instrum., 17, 6-14, (1946).

2.  G. P. Williams, C. J. Hirschmugl, E. M. Kneedler, P. Z. Takacs, et al., Coherence Effects in Long-Wavelength Infrared

Synchrotron Radiation Emission, Phys. Rev. Lett., 62, 261–263, (1989).

3.  F. C. Michel, Intense Coherent Submillimeter Radiation in Electron Storage Rings, Phys. Rev. Lett., 48, 580–583, (1982). 4.  C. J. Hirschmugl, M. Sagurton and G. P. Williams, Multiparticle coherence calculations for synchrotron-radiation

emission, Phys. Rev. A, 44, 1316–1320, (1991).

5.  G. L. Carr, M. C. Martin, W. R. McKinney, K. Jordan, et al., High-power terahertz radiation from relativistic electrons, Nature, 420, 153-156, (2002).

Development of CSR Spectral Simulations

•  In JLab FEL accelerator, we consider 100% of the charge in

each bunch to participate in CSR emission

•  We also assume Gaussian bunch shapes

•  e

-

_{beam is monoenergetic with a very small ΔE/E}

•  We do not expect such idealized conditions at the solar flare site

•  Began to look at the effect on the CSR spectrum if we modified

Varying the Size of the e

-

_Bunches

3000 µm

300 µm

30 µm

100 GHz

1 THz

10 THz

Varying the Shape of the e

-

_Bunches

Gaussian shape

Sech(t/

_τ

_b

) shape

Sech(t/

_τ

_b

) shape has longer tails

Varying the Energy Distribution of the e

-

_Bunches

Consider a Maxwell-Juttner

Distribution with a temperature

of T

_e

= 120 E

_o

/k

_B

peak at ~

γ=240 (120 MeV)

high energy tail of

distribution

increases ISR

cutoff and reduces

slope of spectrum

beyond ISR peak

Varying the Fraction of e

-

_{Participating in CSR Emission}

109 101 1 101 3 101 5 101 7 10- 1 2 10- 9 10- 6 0.001 1 1000 frequency HHzL

N

_CSR

= 10

-4

_N

ISR

N

_CSR

= 10

-8

_N

ISR

N

_ISR

= 10

20

_e

-

CSR Fit to November 4, 2003 Flare

τb = 30 ps (9 mm) τb = 47 ps (14 mm) N_e = 4.5x1029 _e-_{/s N} e = 1.35x1029 e-/s N_CSR = 7.1x10-15 _N e NCSR = 2.15x10-14 Ne

Owens Valley Solar Array (OVSA) and the Solar Submillimeter Telescope (SST)

CSR Fit to December 6, 2006 Solar Flare Burst (18:43:51 UT)

τb = 95 ps (29 mm) τb = 43 ps (13 mm) τb = 65 ps (20 mm) N_e = 3.6x1027 _e-_{/s N} e = 1.5x1029 e-/s Ne = 9.0x1028 e-/s N_CSR = 3.8x10-14 _N e NCSR = 9.8x10-15 Ne NCSR = 2.6x10-14 Ne

Questions/Issues/Comments on Solar Flare Spectrum Fits

•  The previous fits consider that all of the e

-

_{’s have the same}

energy distribution

•  this would seem to be an unreasonable constraint

•  perhaps should use a different distribution (power law)

•  If we consider that measured spectrum/power is produced by

many different sources/regions on the sun

•  it would be better to model emission from many sources,

each with different energy distribution and charge density

•  this creates much greater complexity in flare model

•  Is it reasonable to consider discrete bunches in a flare

accelerator or should we relax this constraint?

(more on this later)

Questions/Issues/Comments on Solar Flare Spectrum Fits

•  Questions remain regarding how to properly address the

angular distribution of CSR radiation

lab

full angular

accelerator = acceptance

(full spectrum)

DESY

The Telegraph

measured spectrum and power depend

on direction of radiation emitted from flare structure

Microbunching Instability as a Path to Flare CSR Emission

M. Venturini and R. Warnock, Bursts of Coherent Synchrotron Radiation in Electron Storage Rings: A

•  At high charge densities, self-interaction processes can cause

microbunching instabilities in the e

-

_beam

•  When this occurs, a burst of powerful CSR emission with a

spectrum related to the small scale density fluctuations is

detected

•  The CSR burst releases

a large amount of

energy from the beam

which redistributes and

smoothes the structure -

reducing the CSR

emission

Microbunching Instability as a Path to Flare CSR Emission

J. M. Byrd, W. P. Leemans, A. Loftsdottir, B. Marcelis, M. C. Martin, W. R. McKinney, F. Sannibale, T.

Scarvie and C. Steier, Observation of Broadband Self-Amplified Spontaneous Coherent Terahertz Synchrotron

•  In lab accelerators, the repetition rate of the bursting CSR

caused by microbunching instabilities has been shown to depend

on the beam current (charge density)

•  A charge density threshold for

microbunching instability has also been

demonstrated, and a similar type of

threshold condition would likely exist

in solar flares

•  This may indicate that CSR emissions

will only be produced from particularly

strong flare sites with very high charge

densities

Microbunching Instability as a Path to Flare CSR Emission

P. Kaufmann, C. G. G. n. d. Castro, E. Correia, J. E. R. Costa, J.-P. Raulin and A. S. V. ́lio, Rapid Pulsations

•  Kaufmann et al. have previously observed bursting emissions

from flare events

•  It was observed that the repetition

rate of bursting is correlated to the

spectral flux, which may be

correlated to the charge density at

the flare site

•  Microbunching instabilities look like

a very reasonable mechanism for

producing small density structures in

solar flare charged particle beams

•  The bursting emissions during flare

events could provide further evidence

of microbunching instabilities

Conclusions

•  We have shown that the CSR emission of broadband coherent

radiation is extremely efficient

•  The peak of the CSR emission depends only on the shape

function

•  of the overall bunch structure of the beam

•  and/or to the small scale charge density fluctuations caused

by microbunching instabilities at high charge densities

•  Bursting emissions may offer further evidence of microbunching

instabilities giving rise to broadband CSR emissions

•  Further studies are ongoing to

•  improve our existing models

•  develop a rigorous model to describe microbunching

instabilities in solar flares

•  Observations with increased spectral coverage will be invaluable

Acknowledgements

Pierre Kaufmann

Jean-Pierre Raulin

(Universidade Presbiteriana Mackenzie)

(CRAAM)

Gwyn Williams (JLab)

Balša Terzić (JLab)

FEL Team (JLab)

New  Particle-­‐in-­‐Cell  Code  For  Numerical  

Simulation  of  Coherent  Synchrotron  Radiation  

Dr.  Balša  Terzić  

Center  for  Advanced  Studies  of  Accelerators  (CASA),  Jefferson  Lab   Center  for  Accelerator  Science  (CAS),  Old  Dominion  University  

 

In  collaboration  with  Rui  Li  (Jefferson  Lab)  and  Matt  Kramer  (UC  Berkeley)  

 

Outline  of  the  Talk  

•  Motivation  and  Background  of  Coherent  Synchrotron  Radiation  (CSR):  

•   Physical  problem  

•     Computational  challenges   •     Two  approaches:    

•     Point-­‐to-­‐Point  (P2P)  and  Particle-­‐In-­‐Cell  (PIC)  

 

•     New  Particle-­‐In-­‐Cell  CSR  Code  

•     Outline  of  the  new  algorithm  

•     New  computational  and  mathematical  methodologies  

•     Parallel  computation  on  Graphical  Processing  Units  (GPUs)   •     Wavelets  

•     First  results:  benchmarking  against  analytical  results  

 

•     Current  Work    

•     Summary      

Coherent  Synchrotron  Radiation:  Motivation  and  Background  

•  When  a  charged  particle  beam  travels  along  a  curved  trajectory,  it  emits          synchrotron  radiation  

•  If  the  wavelength  λ  of  synchrotron  radiation  is  longer  than  the  bunch  length  

σ_s,  the  resulting  radiation  is  coherent  (CSR)                  

•     ISR  radiated  power:       •     CSR  radiated  power:  

σ

_s incoherent  (ISR)   coherent  (CSR)   λ>σ_s λ<σ_s largely     cancels  out   has     systematic     effects   P = e 2 c 6πε0 N m₀c2

(

)

4 E4 R2 P = 2 4/3 31/6_[Γ[2 3]_]2e2 π N2 R2/3σs 4/3 ! $4

•  CSR  is  the  low  frequency  part  of  the  synchrotron  radiation  power  spectrum                                      

•     N  particles  in  the  bunch  act  in  phase  and  enhance  intensity  by  a  factor  N  

     (typically  N=109_-­‐1011₎  

 

Coherent  Synchrotron  Radiation:  Motivation  and  Background  

•  Short  bunch  lengths  are  desirable  in  many  different  contexts:  

•     FEL,  next  generation  light  sources,  ERL,  B-­‐factories,  linear  colliders  such  as  ILC…   •     The  demand  for  short  bunches  is  expected  to  increase  in  the  future  

 

•     This  presents  a  problem:    

                 Short  beam  bunch    ⇒    CSR  is  dominant    ⇒    beam  is  subject  to  adverse  CSR  effects    

•     Adverse  CSR  effects,  which  can  seriously  impair  beam  quality:  

•     Energy  spread  

•     Longitudinal  instability  (microbunching)   •     Emittance  degradation  

 

•     It  is  of  vital  importance  to  have  a  trustworthy  code  to  simulate  and  mitigate  

     the  CSR  effects  

•  Dynamics  of  an  electron  bunch  is  governed  by    

   

•           :    external  EM  fields   •                 :    self-­‐interaction  (CSR)              

Coherent  Synchrotron  Radiation:  Computational  Challenges  

}

retarded     potentials   φ(r, t)  A(r, t) ! " # # $ % & &= ρ(r ', t ')  J (r ', t ') ! " # # $ % & &

∫

d  r '  r −r '

Charge  density:   Need  to  track  the  entire   history  of  the  bunch  

ρ(r, t) =

∫

f (r, v, t) dv  _{    } retarded     time   t ' = t −  r −r ' c  Eself = −∇φ−1 c ∂A ∂t  Bself = ∇ × A d dt γme  v

(

)

= e

(

E + β×B

)

β =  v c  E =Eext +Eself  B = Bext +Bself  Eext, Bext  Eself, Bself LARGE  CANCELLATION   NUMERICAL  NOISE     DUE  TO  GRADIENTS  

•  Storing  and  computing  with  a  4D  (3  positions,  1  time)  charge  and  current          densities  is  prohibitively  expensive  

         Need  simplifications/approximations  

 

•     Possible  simplifications  to  full  dimensional  CSR  modeling:  

•     1D  line  approximation  (IMPACT,  ELEGANT):  too  simplistic  /  often  inaccurate   •     2D  approximation  (vertically  flat  beam):    

   Codes  by  Li  1998,  Bassi  et  al.  2006,  …  

 

•     Based  on  how  the  DF  (and,  consequently,  charge  and  current  densities)    

     are  represented,  two  approaches  emerge:   •     Point-­‐to-­‐point:    

       Solve  Maxwell's  equations  using  retarded  potentials  with  DF  represented            by  macroparticles  

•     Particle-­‐In-­‐Cell  (PIC)  (mean  field,  grid,  mesh):  

       Solve  Maxwell's  equations  or  retarded  potentials  on  the  grid,    

Coherent  Synchrotron  Radiation:  Point-­‐to-­‐Point  Approach  

•  Point-­‐to-­‐Point  approach  (2D):    [Li  1998]                            

•     Charge  density  is  sampled  with  N  Gaussian-­‐shaped  2D  macroparticles        (2D  distribution  without  vertical  spread)  

 

•     Each  macroparticle  interacts  with  each  macroparticle  throughout  history    

•     Expensive:  computation  of  retarded  potentials  and  self  fields  ~  O(N2₎                  ⇒    small  number  N      ⇒      poor  spatial  resolution  

         ⇒    difficult  to  see  small-­‐scale  structure     DF   Charge  density   Current  density   Gaussian  macroparticle   f (r, v, t) = q n_m(r − r₀(i)(t)) i=1 N

∑

δ(v − v₀(i)(t)) ρ(r, t) = q n_m(r − r₀(i)(t)) i=1 N

∑

 J (r, t) = q β0 (i) (t) n_m(r − r₀(i)(t)) i=1 N

∑

n_m(r − r₀(i)(t)) = 1 2πσm 2 exp − (x − x0(t)) 2 + (y − y0(t)) 2 2σm 2 # $ % & ' (

Coherent  Synchrotron  Radiation:  Particle-­‐In-­‐Cell  Approach  

•  Particle-­‐In-­‐Cell  approach  with  retarded  potentials  (2D):                            

•     Charge  and  current  densities  are  sampled  with  N  point-­‐charges  (δ-­‐functions)          and  deposited  on  a  finite  grid              using  a  deposition  scheme      

•     Two  main  deposition  schemes  

       -­‐    

Nearest  Grid  Point  (NGP)  

                 

(constant:  deposits  to  1D  _points)

 

       -­‐    

Cloud-­‐In-­‐Cell  (CIC)  

                 

(linear:  deposits  to  2D  _points)  

         There  exist  higher-­‐order  schemes  

    p( ⃗X) ⃗ x_⃗k NGP   CIC   p(x)   x    –    macroparticle  location   DF  (Klimontovich)   Charge  density   Current  density   f (r, v, t) = q δ(r − r₀(i)(t)) i=1 N

∑

δ(v − v₀(i)(t)) ρ(x k, t) = q δ(  x k −  x₀(i)(t) +X) −h h

∫

i=1 N

∑

p(X) d X  J (x k, t) = q  β0 (i) (t) δ(x k −  x₀(i)(t) +X) −h h

∫

i=1 N

∑

p(X) d X

Coherent  Synchrotron  Radiation:  P2P  Vs.  PIC  

•     Computational  cost  for  P2P:      Total  cost  ~  O(N2)    

•   Integration  over  history  (yields  self-­‐forces):    O(N2_{)  operation}    

•     Computational  cost  for  PIC:      Total  cost  ~  O(N_grid2)    

•   Particle  deposition  (yields  gridded  charge  &  current  densities):  O(N)  operation   •   Integration  over  history  (yields  retarded  potentials):  O(N_grid2_{)  operation}  

•   Finite  difference  (yields  self-­‐forces  on  the  grid):  O(N_grid)  operation  

•   Interpolation  (yields  self-­‐forces  acting  on  each  of  N  particles):  O(N)  operation   •   Overall  ~  O(N_grid2_{)+O(N)  operations}  

•  But  in  realistic  simulations:    N_grid2_{>>  N,  so  the  total  cost  is  ~  O(N}

grid2)  

•   Favorable  scaling  allows  for  larger  N,  and  reasonable  grid  resolution        ⇒    _{Improved  spatial  resolution}  

 

•     Fair  comparison:    P2P  with  N  macroparticles  and  PIC  with  N_grid=N      

Coherent  Synchrotron  Radiation:  P2P  Vs.  PIC    

•  Difference  in  spatial  resolution:  An  illustrative  example      

•  Analytical  distribution  sampled  with     •  N  =  N_XN_Y    macroparticles  (as  in  P2P)   •  On  a  N_x×N_Y    grid  (as  in  PIC)        

•     2D  grid:    N_X=N_Y=32                    

•     PIC  approach  provides  superior  spatial  resolution  to  P2P  approach  

•     This  motivates  us  to  use  a  PIC  code  for  CSR  simulations  

EXACT   P2P    N=322    _{SNR=2.53   PIC    N=50x32}2    _SNR=13.89   Signal-­‐to-­‐Noise  Ratio   SNR = qi 2 i=1 N_grid

∑

qi − qi ( )2 i=1 N_grid

∑

q_i exact q_i grid

N macroparticles

at t=t_k

system  at  t=t_k+∆t  

Advance  particles  by  ∆t  

Distributions  on    

N_x×N_y  grid  for  t=t_k  

N  point-­‐particles  

at  t=t_k   Bin  particles  on    N_x×N_y  grid  

Interpolate  to  obtain  forces    

on  each  particle  

Integrate  over  grid  histories  to   compute  retarded  potentials    

and  corresponding  forces  

on  the  N_x×N_y  grid  

Outline  of  the  PIC  Algorithm  For  CSR  Simulations    

New  PIC  CSR  Code:  Outline    

3  coordinate  frames    

Computing  retarded  potentials:   Major  computational  bottleneck  

New  PIC  CSR  Code:  Outline    

•       Choosing  a  correct  coordinate  system  is  of  crucial  importance  

•  To  simplify  calculations  use  3  frames  of  reference:  

 

•  Frenet  frame  (s,  x)  

 s  –  along  design  orbit  

 x  –  deviation  normal  to                direction  of  motion        -­‐    Particle  push  

 

•  Lab  frame  (X,  Y)  

 -­‐    Integration  range  

     -­‐    Integration  of  retarded                potentials  

 

•  Grid  frame  (X~,Y~)  

Scaled  &  rotated  lab  frame   always  [-­‐0.5,0.5]  ×  [-­‐0.5,0.5]  

New  PIC  CSR  Code:  Particle  Deposition    

•  Grid  resolution  is  specified  a  priori  (fixed  grid)     •     N_X  :  #  of  gridpoints  in  X  

•     N_Y  :  #  of  gridpoints  in  Y   •     N_grid  =  N_X  ×  N_Y  total  gridpts   •     Grid:  

   

•     Inclination  angle  α  

•     Point-­‐particles  deposited  on  

       the  grid  via  deposition  scheme  

           

•     Grid  is  determined  so  as  to  tightly  envelope  all  particles  

     Minimizing  number  of  empty  cells    ⇒    optimizing  spatial  resolution  

X_ij,Y_ij

New  PIC  CSR  Code:  Computing  Retarded  Potentials    

•  Carry  out  integration  over  history:    

•  Determine  limits  of  integration  in  lab  frame:  

 

  compute  Rmax  and    

(θ_mini_{,  θ} maxi)  

For  each  gridpoint,  independently,   do  the  same  integration  over     beam’s  history  

Obvious  candidate  for   parallel  computation  

Parallelization  With  GPUs  

•     Parallel  computation  on  GPUs  is  made  efficient  through:  

•     Use  of  several  ultra-­‐fast,  small  memory  types  (shared,  local,  registers)  

•     No  communication  between  computational  threads  

•     Avoiding  branching  statements  (computational  bottleneck)  

•     Capable  of  executing  thousands  of  simultaneous  computations  (threads)    

CPU  

Parallelization  With  GPUs  

•     Computing  the  retarded  potentials  requires  integrating  over  the  entire    

       bunch  history  –  very  slow!  We  must  parallelize.  

 

•     We  need  to  design  a  new  adaptive  integration  algorithm  so  as  to  best  exploit        advantages  afforded  by  architectural  differences  between  CPUs  and  GPUs    

•     Useful  beyond  this  project  

 

•     Integration  over  a  grid  is  ideally  suited  for  GPUs:  

•     No  need  for  communication  between  gridpoints   •     Same  kernel  executed  for  all  (interpolation)  

•     Can  remove  all  branches  from  the  algorithm  

 

•     We  implemented  GPU-­‐based  integrator  on    

       NVIDIA’s  CUDA  framework  (extension  to  C++)   •     CUDA  enables  computation  on  GPUs  by  breaking            them  down  into  small,  independent  blocks  

 

l  Orthogonal  basis  of  functions  composed  of  scaled  and  translated  versions  of  

the  same  localized  mother  wavelet  

ψ

(x)  and  the  scaling  function  ϕ(x):                    

     

                                                                                                                       

l  Each  new  resolution  level  k  is  orthogonal  to  the  previous  levels  

l  Compact  support:  finite  domain  over  which  nonzero    

l  In  order  to  attain  orthogonality  of  different  scales,  

their  shapes  are  strange  

 -­‐  Suitable  to  represent  irregularly  shaped  functions  

l  For  discrete  signals  (gridded  quantities),  fast    

Discrete  Wavelet  Transform  (DFT)  is  an  O(MN)    

operation,  M  size  of  the  wavelet  filter,  N  signal  size  

Wavelets  

Daubachies  4th  _{order  wavelet}  

ψ_ik(x) = 2k/2ψ(2kx − i), k, i ∈ Z f (x) = s₀0φ₀0(x) + d_ik i

∑

k

∑

ψ_ik(x),

l  Wavelet  basis  functions  have  compact  support  ⇒    signal  localized  in  space  

Wavelet  basis  functions  have  increasing  resolution  levels    

                           ⇒    signal  localized  in  frequency    

 ⇒  Simultaneous  localization  in  space  and  frequency  (FFT  only  frequency)  

l  Wavelet  basis  functions  correlate  well  with  various  signal  types    

(including  signals  with  singularities,  cusps  and  other  irregularities)    

 ⇒  Compact  and  accurate  representation  of  data  (compression)  

l  Wavelet  transform  preserves  hierarchy  of  scales  

l  In  wavelet  space,  discretized  operators  (Laplacian)  are  also  sparse  and  have  an  

efficient  preconditioner    ⇒    Solving  some  PDEs  is  faster  and  more  accurate    

l  Provide  a  natural  setting  for  numerical  noise  removal    ⇒    Wavelet  denoising  

Wavelet  thresholding:      If  |w_ij|<T,    set  w_ij=0.  

 

 [Terzić,  Pogorelov  &  Bohn  2007,  PR  STAB  10,  034201]  

l  When  the  signal  is  known,  one  can    

compute  Signal-­‐to-­‐Noise  Ratio  (SNR):    

 

       N_ppc:  avg.  #  of  particles  per  cell        N_ppc  =  N/N_cells    

2D  superimposed  Gaussians  on  256×256  grid  

                       

Wavelet  Denoising  and  Compression  

ANALYTICAL SNR = q_i2 i=1 Ngrid

∑

q_i − q_i ( )2 i=1 Ngrid

∑

qi exact q_i grid SNR = N_ppc

l  When  the  signal  is  known,  one  can    

compute  Signal-­‐to-­‐Noise  Ratio  (SNR):    

 

       N_ppc:  avg.  #  of  particles  per  cell        N_ppc  =  N/N_cells    

2D  superimposed  Gaussians  on  256×256  grid  

                     

Wavelet  Denoising  and  Compression  

ANALYTICAL N_ppc=3 SNR=2.02 N_ppc=205 SNR=16.89 N_ppc= 3 SNR = 16.83 SNR = q_i2 i=1 Ngrid

∑

q_i − q_i ( )2 i=1 Ngrid

∑

qi exact q_i grid SNR = N_ppc

l  When  the  signal  is  known,  one  can    

compute  Signal-­‐to-­‐Noise  Ratio  (SNR):    

 

       N_ppc:  avg.  #  of  particles  per  cell        N_ppc  =  N/N_cells    

2D  superimposed  Gaussians  on  256×256  grid  

                     

Wavelet  Denoising  and  Compression  

ANALYTICAL N_ppc=3 SNR=2.02 N_ppc=205 SNR=16.89 N_ppc= 3 SNR = 16.83 SNR = q_i2 i=1 Ngrid

∑

q_i − q_i ( )2 i=1 Ngrid

∑

qi exact q_i grid SNR = N_ppc

l  When  the  signal  is  known,  one  can    

compute  Signal-­‐to-­‐Noise  Ratio  (SNR):    

 

       N_ppc:  avg.  #  of  particles  per  cell        N_ppc  =  N/N_cells    

2D  superimposed  Gaussians  on  256×256  grid  

                       

Wavelet  Denoising  and  Compression  

COMPACT: only 0.12% of coeffs

ANALYTICAL N_ppc=3 SNR=2.02 N_ppc=205 SNR=16.89

WAVELET THRESHOLDING

DENOISED

COMPACT: only 0.12% of coeffs

SNR = q_i2 i=1 Ngrid

∑

q_i − q_i ( )2 i=1 Ngrid

∑

qi exact q_i grid SNR = N_ppc N_ppc=3 SNR=16.83

l  When  the  signal  is  known,  one  can    

compute  Signal-­‐to-­‐Noise  Ratio  (SNR):    

 

       N_ppc:  avg.  #  of  particles  per  cell        N_ppc  =  N/N_cells    

2D  superimposed  Gaussians  on  256×256  grid  

                     

Wavelet  denoising  yields  a  representation  which  is:  

-­‐    Appreciably  more  accurate  than  non-­‐denoised  representation  

Wavelet  Denoising  and  Compression  

COMPACT: only 0.12% of coeffs

ANALYTICAL N_ppc=3 SNR=2.02 N_ppc=205 SNR=16.89

WAVELET THRESHOLDING

DENOISED

COMPACT: only 0.12% of coeffs

SNR = q_i2 i=1 Ngrid

∑

q_i − q_i ( )2 i=1 Ngrid

∑

qi exact q_i grid SNR = N_ppc N_ppc=3 SNR=16.83

Wavelet  Compression  

[From  Terzić  &  Bassi  2011,  PR  STAB  14,  070701]  

 

Modulated  flat-­‐top  particle  distribution   _{retained  after  wavelet  thresholding}  Fraction  of  non-­‐zero  coefficients  

1%   0.1%  

New  PIC  CSR  Code:  Large  Cancellation  At  Work    

•  Traditionally  difficult  to  track  large  quantities  which  mostly  cancel  out:    

                               

•       High  accuracy  of  the  implementation  able  to  track  accurately  these  

4

×

10

7  

6

×

10

2  

N=128000   N_x=N_y=32  

Effective  Longitudinal  Force:    Fs

eff  =          ∂sϕ −  βs                ∂sΑs  

ϕ 
 −  β∂_s                s∂_s Α_s  

New  PIC  CSR  Code:  Benchmarking  Against  Analytic  1D  Results  

•   Analytic  steady  state  solution  available  for  a  rigid  line  Gaussian  bunch          [Derbenev  &  Shiltsev  1996]  

                            N=512000   N_x=N_y=64  

Semi-­‐Analytic  2D  Results:  1D  Model  Breaks  Down  

•     Analytic  steady  state  solution  is  justified  for            [Derbenev  &  Shiltsev  1996]  

•     Li,  Legg,  Terzić,  Bisognano  &  Bosch  2011:  

                              κ = σx Rσ_z2

(

)

1/3 << 1

1D  &  2D  disagree  in:          Magnitude  of  CSR  force            Location  of  maximum  force    

 

Model  bunch  compressor  (chicane)  

       E  =  70  MeV  

         σ_z0=  0.5  mm  

         u  =  -­‐10.56  m-­‐1  _{energy  chirp}    

L_b  =  0.3  m   L_B  =  0.6  m   L_d  =  0.4  m  

⇒    _{1D  CSR  model  is  inadequate}    

 

Preliminary  simulations  show   good  agreement  between  2D     semi-­‐analytic  results  and  results   obtained  with  our  new  code  

New  PIC  CSR  Code:  Efforts  Currently  Underway  

l  Compare  to  2D  semi-­‐analytical  results  

   Terzić  &  Li  2012,  in  preparation  (2-­‐3  months  away  from  submission)        

l  Optimize  the  GPU-­‐parallelized  implementation  

Simulate  Jefferson  Lab  FEL  

Document  the  code  and  make  it  freely  available  to  the  community  

   Kramer,  Terzić  &  Li  2012,  in  preparation  (5-­‐6  months  away  from  submission)    

l  Further  Afield:  

l  Computation  of  retarded  potentials  in  wavelet  space  

l  Promises  significant  improvement  in  efficiency  and  memory  overhead   l  Simulation  of  other  existing  and  future  machines  

Summary  

l  Motivated  the  need  for  accurate  CSR  codes  

 

l  Demonstrated  that  the  PIC  approach  is  better  because  of:  

l  Better  spatial  resolution  (a  “must”  for  resolving  small-­‐scale  instabilities)   l  Better  scaling  with  the  number  of  particles  N    

 

l  Presented  the  new  2D  PIC  code:  

l  Resolves  traditional  computational  difficulties  

l  Uses  new  computational  and  mathematical  methodologies:  GPUs  and  Wavelets     l  Presented  a  proof  of  concept:  excellent  agreement  with  analytical  1D  results  

(and  some  preliminary  semi-­‐analytic  2D  results)  

 

l  Closing  in  on  our  goals:    

l  Accurate  and  efficient  code  which  faithfully  simulates  CSR  effects  in  real  machines   l  Being  able  to  quantitatively  simulate  CSR  effects  as  the  first  step  toward  

•  Inter-­‐disciplinary  center  for  accelerator  science  

•  Established  in  2009  

•  Internationally  known  SRF  scientist  Jean  Delayen  as  the  first  director  

(Jefferson  Lab/Old  Dominion  University  joint  appointment)  

•  Hired  a  renowned  SRF  theorist  

•  1  postdoc,  but  searching  for  more  

•  10  graduate  students  pursuing  doctorate  degrees  

•  2  accelerator  physics  courses  offered  

•  A  dedicated  10000  ft2  (930  m2)  building  

•  Accelerator-­‐based  light  sources  

•  High-­‐current  proton  and  deuteron  superconducting  accelerators  

•  Beam  dynamics  of  space-­‐charge  dominated  beams  

•  Advanced  superconducting  materials  for  accelerator  applications  

•  Concepts  and  manufacturing  techniques  for  superconducting  

accelerators  and  their  components  (cavities,  couplers,  tuners,  cryostats,   refrigerators…)  

•  Control  systems  for  high-­‐reliability,  high-­‐availability  particle  accelerators  

•  Simulation  tools  for  particle  accelerators  for  large  (>108)  number  of  

particles,  that  include  space  charge,  static  and  dynamic  errors,  and  are   able  to  realistically  predict  beam  losses  and  activation  

•  Computational  accelerator  physics:  

–  Non-­‐linear  optimization  (genetic,  particle-­‐swarm  algorihtms…)  

–  CSR  simulations  

• 

Hampton  University  

–  Offer  accelerator  physics  courses  to  their  graduate  students  

• 

State  University  of  New  York  

–  Establish  bi-­‐lateral  teaching  and  research  programs  

–  Exchange  of  students  

–  Post-­‐docs   –  Scientists  

• 

International  

–  United  Kingdom   –  China   –  India   –  Brazil?  

CAS  Collaborations  

Two  venues  for  qualified  students:  

 

•  Apply  for  admission  to  one  of  our  member  institutions    

(http://www.sura.org/about/members.html)  

–  For  accelerator  physics,  Virginia  Institutions  are  preferable  due  to  

travel  and  work  logistics    

•  Old  Dominion  University,  Hampton  University,  University  of  

Virginia,  Virginia  Polytechnic  and  State  University    

•  Through  Memoranda  of  Understanding,  do  research  work  at  

Jefferson  Lab,  while  attending  a  Brazilian  institution  

First  choice  has  fewer  hurdles  

Solar sub-THz emission mechanisms Eduard P. Kontar University of Glasgow, UK 18th_{, April 2011} Solar flares From Emslie et al., 2004

Talk outline I) Radio emission – fundamentals

Radio spectrum (Quiet and active Sun) Optical thin/thick emission

Brightness temperature

II) Radio emission mechanisms

Free-free emission Gyromagnetic emission

Plasma emission (collective effects)

III) Quiet Sun radio emissions

Temperature diagnostics of the low atmosphere Magnetic field diagnostics

IV) Active Sun emission and solar flare emission

The tall will not cover all possible mechanisms…

Radio Sun: quiet and active sun 1 10 GHz 0.1 100 Flux, sfu 1000 105 104 103 Typical radio spectrum from a solar flare gyrosynchrotron emission plasma emission 0.01

Ionospheric cut-off ~10 MHz Radio spectrum

quiet Sun 102 1 sfu = 104_Jansky ? Brightness temperature ν h log lo g Iν 2 ν ν ∝ I Rayl eigh - Jea ns max loghν

We can always make a definition, common in radio astronomy: Brightness temperature

⇒ <<kT hν ( ) kT h kT hν −₁≈ ν exp Rayleigh – Jeans approximation

At typical radio frequencies and temperatures Hence ( ) [ ] 2 2 2 3 2 1 exp 2 c kT c hv I kT h ν ν ν = ₋ ≅ k I c T_{b 2} 2 2ν ν =

Optically thick and optically thin emission l d τ l d I dI =− κ I dI I +

If we model the absorption in the slab as:

Absorption coefficient, which is not in general constant, but depends on depth and frequency in the atmosphere

The optical depth, denoted by , so that I = I e−τ

0 obs

If we describe the atmosphere as “transparent” and

If we describe the atmosphere as “optically thin” and

If we describe the atmosphere as “optically thick” and

0 = τ Iobs =I0 0 obs I I ≈ 1 << τ 0 obs I I << 1 ≥ τ

For example, free-free absorption coefficient (Dulk, 1985):

Solar radio emission mechanisms

Free-free emission (collisions of electrons with

protons and other particles)

Gyromagnetic emission(cyclotron and gyrosynchrotron)

Coherent emissiondue to wave and wave-particle interaction

<= gyrofrequency

<= plasma frequency

Free-free emission

Photons are produced by

free-free transitions of electrons – also known as

Bremsstrahlung (‘braking radiation’)

Photon

Frequency Flux density

Optically thick part Optically thin part

Free-free emission from plasma

Free-free emission

A rising spectrum from a compact (20’’) sourcerequires that the source is relatively

dense(n_e~1011_cm−3_{) and hot(T}

e~10 MK). (Fleishman and Kontar, 2010)

Thermal free-free radio spectraproduced from a uniform cubic source with a linear

size of 20’’ for n_e = 1011_{to 4 × 10}12_cm−3_{and T}

e= 0.5–5 MK.

See also Kaufman et al, 2009

Gyro-magnetic emission

Cyclotron Radiation

Any constant velocity component parallel to the magnetic field line

leaves the radiation unaffected (no change in acceleration), and

electron spirals around the field line.

Electron cyclotron line has frequency

Photon

In ultra-relativistic limit, this radiation is known as synchrotron– it is strongly Doppler shifted and forward beameddue to relativistic aberration.

Gyro-magnetic emission S ν ν ~0.3 S ν ν ~

Brightness Temperature and Flux density as a function of frequency for various

emission mechanisms (Dulk, 1985)

Plasma emission mechanisms

Electron Beam Langmuir waves Wave-wave interactions Fundamental Radio emission

Harmonic radio emission Secondary waves

Coherent emissiondue to wave-wave and wave-wave-particle interaction

Plasma emission mechanisms

Fundamental radio emission(at local plasma frequency)

1) Ion-sound decay L=T+S 2) Scattering off ions L+i=T+i

Harmonic radio emission(double plasma frequency)

1) Decay and coalescence L =L’+S, L+L’=T 2) Scattering and coalescence

L+i=L+i’, L+L’=T

Frequency

For each act of decay or coalescence we have the corresponding conservation laws for momentum and energy require:

Flux Emitted

Observed

Multi-frequency Sun

From Grechnev et al, 1998

Chromosphere: Brightness temperature vs frequency

Observed brightness temperature as a function of frequency (from Landi et al, 2008).

Quiet Sun – what can we learn? Radio diagnostics of solar chromosphere and lower

corona:

Free-free emission-> Temperature and Emission measure

Thermal Gyrosynchrotron-> Magnetic fields

Lee et al 1998; Bastian et al, 2006

Solar flares

From Emslie et al., 2004

Flare emission X -r a y s ra d io w a v es P ar ti cl es 1 A U Krucker et al, 2001

Aschwanden and Benz, 1997

Flare emission radio emission

1 10 GHz 0.1 100 Flux, sfu 1000 105 104 103

Typical radio spectrum from a solar flare

gyrosynchrotron emission plasma emission

Flare emission radio emission 1 10 GHz 0.1 100 Flux, sfu 1000 105 104 103

Observations above ~100 GHz e.g. Kaufmann et al. 2001, 2004, 2009, Trottet et al. 2002, 2008; Luthi et al. 2004, 2004; Cristiani et al. 2008; Silva et al. 2007.

Sub-THz emission mechanisms

The main observational characteristics:

•relatively large radiation peak flux

of the order of 104_{sfu (Kaufmann} et al. 2004);

•radiation spectrum rising with

frequencyF(f )∝fδ _{(Trottet, G. et}

al, 2002);

•spectral index varying with time

within δ∼1–6;

•sub-THz component can display a sub-second time variability with the modulation about 5% (Raulin, J.-P. et al, 2003; Kaufmann et al. 2009);

• the source size is believed to be

less than 20’’(however, it is indirect conclusion) (see also Luthi et al. 2004a, 2004b for large source indications)

Sub-THz emission mechanisms

Fleishman & Kontar 2010 consider a list of emission mechanisms, capable of producing a sub-THz

component, both well known and new in this context, and calculate a representative set of their spectra produced by:

(1) free-free emission;

(2) Gyrosynchrotron emission;

(3) Synchrotron emission from relativistic positrons/electrons;

(4) Diffusive radiation (Langmuir waves); (5) Cherenkov emission;

(1) Free-free emission

A rising spectrum from a compact (20’’) sourcerequires that the source is relatively

dense(n_e~1011_cm−3_{) and hot(T}

e~10 MK).

Note, that from the observations we can excludethe option of a source that is both dense

and hot, say n_e∼1012_cm−3_{and T}

e∼10 MK, EM = ne2V ∼3 × 1051cm−3.

Thermal free-free radio spectraproduced from a uniform cubic source with a linear

size of 20’’ for n_e = 1011_{to 4 × 10}12_cm−3_{and T}

e= 0.5–5 MK.

(2) Free-free emission

Temporal pulsations of the free-free emissioncould be MHD oscillations (e.g. sausage mode) of the corresponding magnetic loop is an attractive scenario (e.g., Fleishman et al. 2008).

Sizes:The flux density above the 1000 sfu level requires the thermal electron number density

above 1012_cm-3_{or/and the linear}

size of the source above 20’’. While the observations (Kontar et al, 2008) suggest that electrons deposit their energy in the

chromosphere at the heights 108

cm with relatively high density. Therefore, a flare heated chromosphere could contain small (>2’’) free-free emitting regions with very high density

1013_-1015_cm-3 _{with temperatures}

from 104_{K up to a few 10}5_K.

20-30 keV

70-150 keV

(3) Gyrosynchrotron Emission

(a) Radio spectra produced by GS plus free–freecontributions from a uniform

source with a size of 1 for n_e= 8 × 1012_cm−3_{and B = 800–4400 G.}

(b) Razin-suppressed GS spectra with the Razinfrequency 200 GHz plus the free–free component.