QFELA.Schiavi

University of Rome “La Sapienza”

2005 ICFA Workshop - Erice

Model equations

+transverse terms

+transverse terms

i!!

!z̄= !

1

2"̄3/2

!2!

!#2! i(Aei!

! A!e"i!)!

!A

!z̄+

!A

!z1

=

! 2!

0

d"

2#|!|2e!i" + i$A

Bonifacio, Piovella & Robb, NIMA 543 (2005),645and Proceedings FEL Conference 2005

Expansion in discrete momentum states

!(!, z1, z̄) =1

!

2"

!!

n="!

cn(z1, z̄)ein!

z̄ =z

Lg

z1 =

z ! vt

Lc

Code scheme

FD explicit scheme in space

Runge-Kutta method in time

QFEL1DQFEL2DQFEL3DQFEL QFELMPI

1D Steady state

|A|2

|b|

2D Steady state

Renormalised model: gain

1D

2D

3D

1D

2D

3D

Renormalised model: saturation

x

!x

Lc

Propagation in 2DInitial electron beam density

Seeded SRS

Seeded SRS + field diffraction

Towards QSASE

Computational resources for QSASE

present 1D runs need 1000 points in z when propagation is switched on

400x400 points in the transverse plane

total points ( 5GB of memory)

sustained power of 10 TFlops for 1h run! 6 · 10

8

Boundary condition issuesdifferential operator not properly terminated at the boundary

large number of mesh points in the transverse direction

need for a perfectly absorbing recipe

would reduce by a factor of 10 the resource requirements

Collaborators

R. Bonifacio & N. Piovella, Uni. Milan and INFN

G. Robb,Univ. of Strathclyde, Glasgow

M.Ferrario +QFEL project @ LNF