Interferometer-based white light measurement of neutral rubidium density and gradient at AWAKE Fabian Batsch, Erdem Öz, Mikhail Martyanov CERN / TUM / Max-Planck-Institute for Physics 2 nd Wigner - AWAKE Workshop, Budapest, May 5, 2017 F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Outline Motivation and requirements Measurement method Achieved accuracy Measurements at AWAKE Summary F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Motivation • Central part in AWAKE: 10 m long rubidium plasma source, n = 10 14 - 10 15 cm -3 • Full laser-ionization of Rb vapor -> plasma with same density Measure instead vapor density at both ends • Linear density ramp of 0-10 % in plasma cell used to optimize e - acceleration process • Gradient set and controlled by Rb reservoir temperatures at both cell ends with better 1 % accuracy Goal: Measure optically Rb vapor density at both ends with ± 0.5% relative accuracy and in a fully automated way ɣ, p + , e - Fig. Drawing of the Rb vapor source (by Diagnostic G.Plyushchev) viewports F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Motivation • Central part in AWAKE: 10 m long rubidium plasma source, n = 10 14 - 10 15 cm -3 • Full laser-ionization of Rb vapor -> plasma with same density Measure instead vapor density at both ends • Linear density ramp of 0-10 % in plasma cell used to optimize e - acceleration process • Gradient set and controlled by Rb reservoir temperatures at both cell ends with better 1 % accuracy Goal: Measure optically Rb vapor density at both ends with ± 0.5% relative accuracy and in a fully automated way From: AWAKE Status Report 2016 F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Motivation • Central part in AWAKE: 10 m long rubidium plasma source, n = 10 14 - 10 15 cm -3 • Full laser-ionization of Rb vapor -> plasma with same density Measure instead vapor density at both ends • Linear density ramp of 0-10 % in plasma cell used to optimize e - acceleration process • Gradient set and controlled by Rb reservoir temperatures at both cell ends with better 1 % accuracy Goal: Measure optically Rb vapor density at both ends with ± 0.5% relative accuracy and in a fully automated way n 1 = ?? n 2 = ?? gradient= ?? F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Outline Motivation and requirements Measurement method Achieved accuracy Measurements at AWAKE Summary F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Properties of Rb Vapor Vapor temperatures of 150°C to Optical transitions from ground state at 200°C, corresponding to a density 780.24 nm (D 2 line) and 794.98 nm (D 1 ) range of 10 14 - 10 15 cm -3 Anomalous dispersion and absorption Vapor density n(T) from vapor in their vicinity pressure curve (5% abs. accuracy): Real and imaginary parts for relative permittivity change n 1 ir 1 N N 1 3 n ( T ) exp( A BT C log( T ) DT ) GS Vapor k T B A,B,C,D material- Index of refraction n ir dependant constants D 2 D 1 Fig. Rb Vapor temperature plotted versus its density Fig. Index of refraction for n= 9.8 . 10 14 cm -3 F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Measurement Method Use interferometry and the hook Fringes equidistant for n Rb = 0 method adapted to vertical fringes Main set-up components: coherent white light source, Mach-Zehnder- interferometer and spectrometer Optical single mode fibers guide light 1 With Rb vapor, anomalous dispersion Fiber collimators allows for free space I ( ) causes density-dependant change in travel through Rb periodicity of interference maxima. 1 I ( ) D 2 2 I ( ) Wavelength [nm] Index of refraction Fig. Setup of the fiber-based Mach- Zehnder Interferometer I tot ( ) I ( ) I ( ) 2 I I cos( ) Wavelength [nm] 1 2 1 2 F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Determine density by fitting Analyze intensity spectrum I tot : Before fit, normalize intensity spectrum to compensate inhomogeneous light Use 1D spectrograph distribution (caused by light source, light transport in fiber): I tot ( λ ) Fig. Interferogram for n= 0 cm -3 Normalization by recording arm spectra or by spectrograph signal conditioning using FFT (by M. Martyanov, does not require reference spectra / noise filtered) possible I tot ( ) I ( ) I ( ) 2 I ( ) I ( ) cos( ) 1 2 1 2 F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Determine density by fitting Analyze intensity spectrum I tot : Before fit, normalize intensity spectrum to compensate inhomogeneous light Use 1D spectrograph distribution (caused by light source, light transport in fiber): • for n Rb = 0 I tot ( λ ) • for n Rb = 5 x 10 14 cm -3 I tot ( ) I ( ) I ( ) 2 I ( ) I ( ) cos( ) 1 2 1 2 F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Determine density by fitting Norm. by arm spectra Look at both transition lines for analysis D 2 D 1 Intensity function S described by: ~ ~ 3 3 ~ 2 n l r f n l r f ~ 0 1 1 0 2 2 S ( ) A cos 4 ( ) 4 ( ) 1 2 S( λ ) with A the amplitude, nl the density-length product λ 1,2 transition wavelength Fitting parameters r 0 classical e - radius marked with ~ f 1,2 oscillation strength path length difference in interferometer Density value obtained by fitting intensity spectrum near transition line , with A, n , fitting parameters Areas ignored by fit F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Determine density by fitting Norm. by FFT Look at both transition lines for analysis Intensity function S described by: ~ ~ 3 3 ~ 2 n l r f n l r f ~ 0 1 1 0 2 2 S ( ) A cos 4 ( ) 4 ( ) 1 2 with A the amplitude, nl the density-length product λ 1,2 transition wavelength r 0 classical e - radius Fitting f 1,2 oscillation strength parameters marked path length difference in with ~ interferometer Density value obtained by fitting intensity spectrum near transition line, with A, n , fitting parameters Dispersion might effect fitting -> completely equal arms Areas ignored by fit F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Automation of the system at CERN: Laser: runs with constant power 24/7 Interferometer : Flippers in both arms, to block and record arms separately, path length difference constant for all measurements Spectrograph : Remotely controlled, software acquires data with both spectrographs simultaneously, saved on local computer Data analysis : CERN FileReader reads-in up- and downstream data for density calculation (done in a FESA class) -> density displayed in control room, density- time file saved in data base (implementation ongoing) F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Outline Motivation and requirements Measurement method Achieved accuracy Measurements at AWAKE Summary F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Two different Rb test cells at MPP: Oil-heated Rb reservoir with a Electrically heated pipe system with temperature stability of 0.1 K l = 51 cm and valves to control Rb flow Vapor column length l = 8 cm (a) pipe Valve (b) Photo: E.Öz E. Öz, F. Batsch, P. Muggli, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.02.005 Rb Valve Cold trap F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Evaluation of the absolute accuracy Norm. by arm spectra Absolute accuracy measured by using a temperature - stabilized Rb vapor source: From vapor pressure curve: 1 1 3 n ( T ) exp( A BT C log( T ) DT ) k T B A,B,C,D material-dependant constants Measured n Rb vs. T : ± 5 % line Measured values tracks vapor pressure curve at 0.6 – 3.8 % level F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Gradient determination accuracy: Norm. by arm spectra Crucial point: Measure not one, but two density - length products with the same accuracy < ± 0.5% <-> determine density gradient at (sub-) % level Idea: Probing the same Rb vapor with two independent measurement setups to simulate to equal vapor column length Interferometer test setup: F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
Results for the relative accuracy: Norm. by arm spectra Record images at const. n, arm 1 (2) corresponds to spectrograph 1 (2): Result: Both measurements differ by 0.1 % (up to 0.3 % , depending on temperature): ARM 2 + 0.5 % ARM 1 - 0.5 % Fig. Results for T = 190 ° C, l=51 cm F. Batsch 2. Wigner - MPP - AWAKE Workshop May 05, 2017
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