Report

Study of X-ray Harmonics of the Polarized Inverse Compton Scattering Experiment at UCLA Adnan Doyurana, Joel Englanda , Chan Joshib , Pietro Musumecia , James Rosenzweiga, Sergei Tochitskyb , Gil Travisha, Oliver Williamsa a UCLA/Particle b Beam Physics Laboratory UCLA/Laser Plasma Group Los Angeles, CA 90034, USA PBPL Particle Beam Physics Lab UCLA Introduction a0 e A0 me c 2 a0 is the normalized amplitude of the vector potential of the incident laser field (just like K, undulator parameter) a0 0.85 10 0 [m] I 0 [W / m ] 5 2 I0 is the intensity and 0 is the wavelength of the incident laser 0 2 2 (1 z 0 ) 2 a 2 1 0 0 2 2 Frequency of the scattered photons where 0 is the frequency of the incident laser, 0 is the relativistic factor of electron beam, z0 is component of the electron initial velocity in the direction of laser pulse. (z0=1 for head on scattering and z0=0 for 90o scattering. PBPL Particle Beam Physics Lab UCLA rb ICS Calculations N N0 3 N 0 a0 2 (1 z ) c T 0 2 (1 a 0 / 2)(1 z 0 ) The total number of photons radiated (1 z ) Where N0 is the number of periods of the laser field with which electrons interacts z 0 a0 2 / 4 0 h0 z 2 1 a0 / 4 0 h0 = 1/137 by a single electron the average axial electron velocity Fine structure constant h0 0 (1 z 0 ) L0 2 Z r 2 w0 1 T min( , , ) Interaction time c 1 z z 0 w0 2 Rayleigh range where w0 is the waist radius of the laser Zr 0 PBPL Particle Beam Physics Lab UCLA Gaussian beam w 2 w0 zM w( z ) w0 1 Z r 2 2 1 F# 2M 2 Radius of the beam PBPL Particle Beam Physics Lab UCLA Zr 0 F number is f/D ~z/2w(z) Incident Laser focusing properties 75 mm waist radius using an F3 and 50 mm waist radius using F2 focusing geometries are achieved experimentally in Neptune. The M factor is estimated to be 1.93. For F2 geometry the Rayleigh range is 0.75 mm. 500 GW laser yields an intensity of 1.25x1016 W/cm2 and a0 1 . Since a0 is proportional to 0 wavelength it is advantageous to use CO2 laser compared to YAG lasers. For F3 geometry the Rayleigh range is 1.7 mm. 500 GW laser yields an intensity of 5.5x1015 W/cm2 and a0 0.67 . PBPL Particle Beam Physics Lab UCLA Time duration of the scattered photons For head configuration the pulse duration will be determined by either the electron bunch length if Lb<L0, Zr or by the pulse length of the laser pulse if electron bunch length is longer than the laser pulse length. So we can express the duration of the scattered photons as 1 min[ Lb , ( 4 Z r L0 )] c For transverse scattering duration of the scattered photons is again determined by electron bunch length if electron is short or by transverse dimension and Rayleigh range of the laser pulse along with the pulse length if electron is long. Thus we can express duration of scattered photons as 1 min[ Lb ,2Z r L0 , L0 2 rb ] c PBPL Particle Beam Physics Lab UCLA Inverse Compton Scattering Experiment Design Parameters Electron and Laser Beam Parameters TABLE 1). Electron and Laser Beam Parameters Parameter Electron Beam Energy Value Beam Emittance Electron Beam Spot size (RMS) Beam Charge Bunch Length (RMS) Laser Beam size at IP (RMS) CO2 laser wavelength CO2 laser Rayleigh range CO2 laser power CO2 laser pulse length PBPL Particle Beam Physics Lab UCLA 14 MeV 5 mm-mrad 25 mm 300 pC 4 ps 25 mm 10.6 mm 0.75 mm 500 GW 200 ps Design Scattered Photon Properties Head-on scattering Transverse scattering Parameter Value Parameter Scattered photon wavelength 5.3 nm Scattered photon wavelength 10.7 nm Scattered photon energy 117.7 eV Scattered photon energy 235.3 eV Scattered photon pulse duration (FWHM) Interaction time 10 ps Number of periods that electrons see (N0) Number of photons emitted per electron (N) 283 Total number of photons Half Opening Angle Bandwidth PBPL Particle Beam Physics Lab 5 ps 3.34 6.3.109 2.7 mrad 10 % UCLA Scattered photon pulse duration (FWHM) Interaction time Number of periods that electrons see (N0) Number of photons emitted per electron (N) Total number of photons Half Opening Angle Bandwidth Value 10 ps 0.33 ps 10 0.11 2.108 15 mrad 10 % Nonlinear Harmonics n n 1 n N0 Bandwidth where N0 is the number of periods that electrons interact. 10% bandwidth is estimated for the fundamental (1 a0 / 2) 2 2 n Half opening angle of the harmonics 15 mrad half angle is estimated 0 n 2 2 (1 z 0 ) n 2 a0 1 2 2 2 Frequency of harmonics PBPL Particle Beam Physics Lab s n Wavelength of harmonics UCLA Double Differential Spectrum of Nonlinear Harmonics 2 d In e k0 sin k 0 2 2 2 [ A J A ( J / b ) ] 2 n t 1 n d d c k 2 2 2 Radiation Spectrum for circularly polarized laser beam* 2 e k0 sin k 0 k g b1 b2 2 [ B B 2 B ] 0 1 2 d d 4 2 c k k0 2 2 d I n 2 2 e k0 sin k 0 b1 b2 2 [ B 2 B ] 1 2 d d 4 2 c k 2 2 d I n 2 2 d 2I n d d d 2 I n d d d 2 I n d d Radiation Spectrum for linearly polarized laser beam* *Ride, Esarey, Baine, Phys. Rev. E, Vol 52, p 5425 (1995) PBPL Particle Beam Physics Lab UCLA 2 Note: All the variables are defined in the paper DDS plots for circularly polarized laser n=1 n=2 n=3 1800 geometry n=1 n=2 n=3 900 geometry PBPL Particle Beam Physics Lab UCLA DDS plots for linearly polarized laser n=1 n=2 n=3 1800 geometry n=1 n=2 n=3 900 geometry parallel polarization n=1 n=2 n=3 900 geometry perpendicular polarization PBPL Particle Beam Physics Lab UCLA Permanent Magnet Quadrupole (PMQ) System for Final Focus Four permanent magnet cubes (NdFeB) are positioned to produce Quadrupole field at the axis. Radia Program is used to design the magnet to produce 110 T/m gradient. Octagonal iron yoke provide proper field flow and hyperbolic iron tips produce perfect quadrupole field inside the magnet. The prototype was build and it is good agreement with the simulation. 1% field error in the magnetization of the cubes in worst orientation causes 10 mm axis offset which is quite reasonable. The cubes are measured and sorted to reduce possible errors. PBPL Particle Beam Physics Lab UCLA Beam Transport for Inverse Compton Scattering IP PBPL Particle Beam Physics Lab UCLA F-Cup Permanent Magnet Dipole (PMD) for Energy Spectrometer Field distribution inside the PMD gap simulated by Radia A Permanent magnet Dipole is designed to serve as energy spectrometer and dump for the electron beam. It bends the beam by 90o. The geometry is chosen so that beam always exits the dipole at 90 o for various energies only with some offset. Iron Yoke is designed for proper field flow Magnets are made out of NdFeB high grade magnets which can yield 1.2-1.4 T magnetization. The Magnetic field inside the gap is ~0.85 T. For 14 MeV energy design electrons the bend radius is about 55mm PBPL Particle Beam Physics Lab UCLA Trajectory in the PMD Trajectory of the electron beam in PMD Angle of the trajectory Inside the Magnet X[mm] X`[rad] Inside the Magnet Outside the Magnet Outside the magnet Trajectory of the 14 MeV electron beam in the PMD gap. Beam enters the magnet by 45 o angle and exits by 45 o angle. Y axis is the length of the magnet and x axis is width. PBPL Particle Beam Physics Lab UCLA Angle of the 14 MeV electron trajectory in the PMD gap. Angle linearly changes from /4 to -/4 inside the magnet. ICS Box design PBPL Particle Beam Physics Lab UCLA Current Status PBPL PMQ design is complete and manufacturing is underway PMD design is complete and manufacturing is in progress Box design is in progress Soft X-ray camera may come from Argonne Polarization measurement is being researched Particle Beam Physics Lab UCLA