High Intensity Synchrotron Radiation Effects Yusuke Suetsugu KEK - PowerPoint PPT Presentation

High Intensity Synchrotron Radiation Effects Yusuke Suetsugu KEK Accelerator School –SR and vacuum system

Introduction Recent high-power (that is, high-currents and high- energies) accelerators generate intense synchrotron radiation (SR). It is a good photon source, but, on the other hand, it has potentially harmful effects on the accelerator performance;  Damage of beam pipes or instruments Heat load  Short lifetime, Noise to particle detectors Gas load  Beam instabilities, Gas load Electron emission …… In this lecture, basic and practical matters to understand above three effects, and how to treat these problems, that is, to protect the machine in a broad sense, are presented. These problems are especially important for the vacuum system of accelerators, but they have widespread effects on machine performances. The understanding of those should be also useful in designing and constructing accelerators. Accelerator School - Synchrotron Radiation Effects 2

Contents About synchrotron radiation (SR) Basic concepts and some important formula Effects of SR Heat load Gas load Electron emission Mechanism, properties and countermeasures Summary Accelerator School - Synchrotron Radiation Effects 3

Synchrotron radiation What is the synchrotron radiation (SR)? Electro-magnetic wave emitted when a high- energy charged particle is accelerated to the orthogonal direction to the velocity, such as a case in a magnetic field. General features of SR High intensity, high photon flux Wide range in wave lengths, from infrared to hard X-ray Well understood spectrum intensity High brightness High polarization ratio and so on Useful as a photon source Accelerator School - Synchrotron Radiation Effects 4

Synchrotron radiation An accelerated charged particle emits electro-magnetic radiation. The radiation fields are given by       : Scalar potential         E A B A A : Vector potential  t Here the retarded Lienard-Wiechert potentials are given by      e     A ( t )      4 c   R ( 1 n ) 0 ret   e 1      ( ) t        4 ( 1 ) R n 0 ret  where R ( ret t ) is the distance vector form source to observer,   and t ct ct R ( ret t ) is the retarded time ret ret Accelerator School - Synchrotron Radiation Effects 5

Synchrotron radiation Electric and magnetic fields are finally given by   ret    1   B n E c                            2 e 1 n e n n           E       3 3           4 4 c 2     R 1 n R 1 n 0 0 ret ret Coulomb field Radiation field  1/ R 2  1/ R At points far from emitting point, the radiation field (  1/ R ) is   more important. ( ret ) ct ct R t ret Accelerator School - Synchrotron Radiation Effects 6

Synchrotron radiation Power of radiation per unit solid angle Pointing vector = Radiation energy flow toward R per unit area.              1 1            2 2 S ( t ) E B E 1 n n cE 1 n n   r 0 c ret 0 0 ret Then, the instantaneous differential radiation power per unit solid angle is         2       n n     2   dP e         2 2 2 n S R cE 1 n R        0 2 5    d 16 c ret ret 1 n 0 ret Accelerator School - Synchrotron Radiation Effects 7

Synchrotron radiation Beaming    2 2 2 dP e sin    If  is parallel to         2 5 d 16 c 1 cos 0              2 2 2 2 2 dP e 1 cos 1 sin  If  is orthogonal to           2 5 16 d c 1 cos 0 5       When  1 , for  0 , then the power 1 cos 0 beams to the front of orbit.  Beaming Angle of beaming  is given by Electric line of force Lorentz factor Accelerator School - Synchrotron Radiation Effects 8

Synchrotron radiation Beaming      //   = 1,  = 0  = 1.5,  = 0.75  = 2,  = 0.87  = 3,  = 0.94        E = 0.551 MeV E = 2.5 MeV E = 5.0 MeV Accelerator School - Synchrotron Radiation Effects 9

Synchrotron radiation Now, consider a charged particle in homogeneous field B. The acceleration in B is given by Centripetal force where the bending radius of charged particle,  , at energy E e is 1 eBc B [ T ]   0 . 2998    [ m ] E E [ GeV ] e e Larmor radius Then the instantaneous radiation power becomes   2 4 4 4 cC 2 cr m c E    e e e P    2 2 3 2 (For electrons)  4 r m     5 e C 8 . 85 10    3 3 3 2 GeV m c e Classical electron radius Accelerator School - Synchrotron Radiation Effects 10

Synchrotron radiation Mass dependence of power Radiation power depends on the mass of the radiating particle like 1/ m 4 . For protons and electrons of the same total energy. Synchrotron radiation is much more important for electron and positron ring. Note that, for superconducting system, such as LHC, the SR is important even proton beams, since the heating might have a significant effect to the cryogenics system. Hereafter, we consider the case of an electron or a positron deflected by a dipole magnet. Accelerator School - Synchrotron Radiation Effects 11

Synchrotron radiation Total power The radiation along a ring per electron is Ring   C 1 1 e         4 U P dt E ds      0 2 2 2   x y For an isomagnetic magnetic field (  = const. ), 4 E U  e C   0 For a circulating beam current I e , the total radiation power P Ie is 4 I E I     e e e P U C   Ie 0 e e Accelerator School - Synchrotron Radiation Effects 12

Synchrotron radiation Total power Ring The total radiation power C : Circumference 4 I E I     e e e P U C   Ie 0 e e The average power line density along the ring is obtained by The power in an angle of  Accelerator School - Synchrotron Radiation Effects 13

Synchrotron radiation Frequency spectrum of power Frequency spectrum is obtained by Furrier transform of E ( t ) .   dW dP t 1     1     ~ 2         2 dt RE dt R E d         d d c c 0 0 The frequency spectrum of power is given by   2 2   d W 1 ~   1    2 i     t R E RE e dt       d d c 2 c 0 0   2         2       n n      R ( t ' ) 2    e   i t '       c    e dt '    5 3      16 c   1 n 0     ret Accelerator School - Synchrotron Radiation Effects 14

Synchrotron radiation The spatial and spectral energy distribution per unit frequency and solid angle is  2 2 2 d W e      2 2 K ( ) F ( , )      2 / 3 3 2 16 d d c 0 c           2 2 2 K ( ) 1 2 3 / 2             2 2 2 2 1 / 3   1 F ( , ) 1 1      2 2 2   2 1 K ( ) c 2 / 3 where K i (  ) is the modified Bessel function, and is the critical frequency. The frequency that halves the total energy Accelerator School - Synchrotron Radiation Effects 15

Synchrotron radiation The photon number (photon flux) with a beam current I e per unit solid angle and frequency is given by Plank’s constant  2 2 2 d N d P 1 d W I 1   ph , Ie Ie e          ( / ) d d d d d d e The spatial and spectral photon flux distribution per unit solid angle and band width (Brightness) is given   3 2 d N     ph , Ie 2 2 C E I K ( ) F ( , )       e 2 / 3 2 d d ( d / ) c Fine-structure  3 photons constant    22 C 1 . 3255 10   2 2 2 2 2 4 e ( m c ) s rad GeV A e photons   13 1 . 3255 10 2 2 s mrad GeV A 0.1%bandwi dth A key parameter of light (photon) sources. Accelerator School - Synchrotron Radiation Effects 16

Synchrotron radiation Example of Brightness Critical energy Example of Super KEKB Mean photon energy 8    c 15 3 Total photon flux 15 3 P   tot N  ph 8 c Accelerator School - Synchrotron Radiation Effects 17