# Presentation: 587646

## Generating THz in Storage Rings.

**Part II**

**Fernando Sannibale**

##  CSR by seeding the microbunching instability. 

** ****CSR by seeding the microbunching instability. **

** ****CSR from "femtoslicing".**

## In operation at the ALS since 1999, and in the last few years also at BESSY II, SLS and UVSOR, ...

**In operation at the ALS since 1999, and in the last few years also at BESSY II, SLS and UVSOR, ...**

-  A. A. Zholents, M. S. Zolotorev, Phys. Rev. Lett. **76**, 912, (1996)

**Beamline optimized for the generation of femtosecond x-ray pulses**

## For a few GeV electron beam, laser pulses with several mJ per pulse are required. This limits the max rep-rate to the order of few KHz

**For a few GeV electron beam, laser pulses with several mJ per pulse are required. This limits the max rep-rate to the order of few KHz**

## The density modulation quickly smears out.

**(In about one turn for the ALS case where ***********C***** = 1.37 ****x**** 10****-3****)**

**For an off-energy particle initially on the reference orbit and for:**

**But by definition:**

**Because of this dispersion term the laser induced energy modulation translates into a longitudinal density modulation.**

## The characteristic length of these density modulations is about the laser pulse length (~100 fs) after the energy modulation, becomes of the order of the ps after ~ a turn and it is completely absorbed by the bunch in the next few turns. 

**The characteristic length of these density modulations is about the laser pulse length (~100 fs) after the energy modulation, becomes of the order of the ps after ~ a turn and it is completely absorbed by the bunch in the next few turns. **

**Such density modulation radiate intense CSR in the THz frequency range**

## BL 5.3.1: provisional THz Port (~ 3 x 3 mrad2 acceptance)

| Parameter  | BL 5.3.1 | BL 1.4 |
| --- | --- | --- |
| Modulation-observation
point distance [m] | 8.4 | 149.5 |
| Energy [GeV] | up to 1.9 |  |
| Current per bunch [mA] | up to 30 |  |
| Ring length [m] | 196.7 |  |
| Dipole bending radius [m] | 4.957 |  |
| Nominal momentum compaction | 0.00137 |  |
| Relative energy spread | 0.001 |  |
| Relative energy modulation | 0.006 |  |
| Laser pulse duration FWHM [fs] | 75 |  |
| Laser repetition rate [pps] | 1000 |  |

**BL 5.3.1: provisional THz Port (~ 3 x 3 mrad****2**** acceptance)**

**BL 1.4: ALS IR beamline (~ 40 x 10 mrad****2**** acceptance)**

##  FTIR spectrometer: IFS 66V, Bruker. 

** ****FTIR spectrometer: ****IFS 66V, *****Bruker*****.**** **
** ****Bolometer: 4.3 K He, HD3, *****Infrared Laboratories Inc*****. **
**  ****BW ~ 1 KHz  -  Frequency response from ~ 5 – 200 cm****-1**
** ****Lock-in amplifier: SR844, *****SRS***

## The 1 kHz structure due to the slicing laser repetition rate is clearly visible.

**The 1 kHz structure due to the slicing laser repetition rate is clearly visible.**
**By switching off the laser the signal disappears**

**The CSR signal is now one of the main diagnostics for the tune-up for the slicing experiment.**

**THz CSR pulses during slicing were indeed measured at the ALS.**
**The figure shows the bolometer signal measured at the two different beamlines in the ring.**

- (J.M.Byrd *et al*., PRL **96**, 164801, 2006.)

## The agreement with calculations is reasonable, but the quality of the measured spectra is poor...

- K. Holldack *et al.*, PRL **96**, 054801 (2006) and K. Holldack *et al.*, PRST-AB **8**, 040704 (2005).

**Similar results (but with better quality spectra!) have been obtained at BESSY II:**

## BL 5.3.1 Spectra:

** ****Instrumentation bandwidth**
** ****Vacuum chamber cutoff**

**Only the high frequency part of the spectrum can be measured**

**BL 1.4 Spectra:**

** ****Fine structure due to water absorption.**

** ****Larger structure due to interference with the vacuum chamber (‘Waveguide effect’).**

## Qualitative agreement.

**Wavefront for photons with wavenumber**
**of 50 cm****-1**** at the window position**

**Qualitative agreement.**
**Actual geometry difficult to simulate.**

## The CSR spectrum and intensity can be controlled by acting on slicing parameters such as:

**The CSR spectrum and intensity can be controlled by acting on slicing parameters such as:**

** ****modulating laser pulse width**

** ****modulating laser intensity**

** ****storage ring momentum compaction**

** ****bunch current**

** ****distance modulator-radiator**

##  Energy per pulse: 8.5 J 

- Physics Retreat, Sept. 22, 04

** ****Laser Modulation: 6 times the ****	****	****      energy spread**
** ****Laser pulse width: 50 fs FWHM**
** ****Distance modulator-radiator: 2.5 m**
** ****Current per bunch: 10 mA**
** ****Horizontal Acceptance 100 mrad ****	****                    (single mode)**

** ****Energy per pulse: 8.5 ********J **
** ****Electric field ~ 1 MV/cm**
** ****Rep. rate: 10 - 100 kHz**
** ****Pulse shaping capability**

## In the described femtoslicing experiment, several mutually synchronous photon beams with very different wavelengths are simultaneously available:

**In the described femtoslicing experiment, several ****mutually synchronous**** photon beams with very different wavelengths are simultaneously available:**

** ****THz CSR synchrotron radiation pulse with transform limited length**

**This opens the possibility for many interesting combinations of "****pump and probe****" experiments where one of the beams is used for exciting the sample while another is used for measuring its characteristics during the excitation transient.**
**By varying the delay between the pulses, one can reconstruct the whole sample response with resolution of the order of ~ 100 fs.**

** ****x-ray pulses with ~ 100 fs length**

** ****Near-IR or visible ~ 100 fs pulse from the slicing laser**

## Self-synchronized Electro-optic sampling

**Self-synchronized Electro-optic sampling**
** ****provides functionality of benchtop setup w/1.5 GHz rep-rate**
** ****use inherent synchronization of optical and THz beams**
** ****optical source can be dipole (very weak) or undulator**
** ****self-mixing techniques also possible.**

## In our case, because the input pulses are coherent, it is possible in principle to resonate the signals to gain high pulse power levels at a reduced repetition rate. 

- T. Smith, et al., NIMA 393 (1997) 245-251.

**In our case, because the input pulses are coherent, it is possible in principle to resonate the signals to gain high pulse power levels at a reduced repetition rate. **

**Peak power limited by cavity Q and phase stability of pulses**

**Experiments interested in exciting samples in the ****nonlinear regime**** require ****electric fields on the sample >~ 1 MV/cm****. Such fields can be obtained by focusing photon ****pulses of energy >~ 10 ********J**** down to their diffraction limited beam size.**

## The example shows how by using a train of laser pulses instead of one single pulse one can concentrate the CSR power within a narrow bandwidth.

**The example shows how by using a train of laser pulses instead of one single pulse one can concentrate the CSR power within a narrow bandwidth.**
**The number of pulses defines the bandwidth while the distance between pulses defines the central frequency of  the peak.**

**One additional interesting possibility of this scheme is the ability of tailoring the electric field of a terahertz pulse by an appropriate shaping of the slicing laser pulse.**

- (J.M.Byrd *et al*., PRL **96**, 164801, 2006.)

**An example of application that could benefit from this capability is the control of complex chemical reactions where the shape of the exciting radiation is dynamically adjusted for optimizing the reaction.**

**In principle by this technique, arbitrary spectrum shapes can be obtained **

## A. Mochihashi et al., UVSOR Workshop on THz CSR (September 2007) 

**A. Mochihashi *****et al.*****, UVSOR Workshop on THz CSR (September 2007) **

## The slicing laser repetition rate is 1 kHz

**The slicing laser repetition rate is 1 kHz**

**During the experiments for characterizing the CSR from femtoslicing, we discovered that if the beam is sliced **_**above**_** the MBI threshold the instability can be seeded.**

**The figure shows the signal as measured from the bolometer. The CSR THz bursts associated with the microbunching instability (MBI) are clearly visible**

**The bursts appearance is usually random (top part) but when the slicing laser is turned on most of the burst become synchronous with the laser (bottom part).**

## The CSR power correlated with the laser slicing scales exponentially with the current per bunch.

**The CSR power correlated with the laser slicing scales **_**exponentially**_** with the current per bunch.**

**The slicing does not impact the dependency of the MBI from current but makes it synchronous with the slicing (1 kHz harmonics)**

**The figures on top show the Fourier transform of the bolometer signal.**

## kHz line Power: ~ quadratic with current below MBI threshold

**Total Power:**** ****~ flat below MBI threshold**

## The measurement is very reproducible.

**The measured saturation is real.****It is not due to the strumentation.**

**Cutting by ~ one half the signal at the bolometer input cuts the signal amplitude by the same amount**

##  The correlated bursts do not start immediately after the slicing.

**Hot electron bolometer ~800 kHz BW, ~10 – 1000 cm****-1**** frequency response (*****Infrared Laboratories Inc*****.)**

** ****In this particular case the correlated bursts peaks after     ~ 45 ********s.**

**Sample Mode**

**Average Mode**

**CSR from slicing**

**CSR from slicing**

**Correlated Bursts**

**Bursts**

## BESSY II observed the same phenomenon.

**BESSY II observed the same phenomenon.**

**Single bunch 7 mA**
**MBI threshold ~ 3.5 mA.**

## In the framework of  the Heifets-Stupakov MBI theory (PRST-AB 5, 054402, 2002) the micro-bunching can be represented by the linear combination of “modes”  with shape:

**In the framework of  the Heifets-Stupakov MBI theory (PRST-AB 5, 054402, 2002) the micro-bunching can be represented by the linear combination of “modes”  with shape:**

**In the “cold beam” approximation, the authors derived an analytical expression for the dispersion function between ********** and *****k*****=2**********/**********. **

**From that, the growth rate *****a *****and the velocity *****v***** for the mode can be calculated:**

**These last two equations show that the unstable mode when excited (by noise or seeding) starts moving along the beam with velocity *****v***** and grows exponentially with rate *****a*****.**

## The accurate analysis of the microbunch evolution should be done (and in fact has been done by Heifets and Stupakov, SLAC-PUB-11815, 2006) by considering the sum of all the unstable modes at that current.

**The accurate analysis of the microbunch evolution should be done (and in fact has been done by Heifets and Stupakov, SLAC-PUB-11815, 2006) by considering the sum of all the unstable modes at that current.**

**In a more simplified analysis, we will assume that one mode is dominant (the one with the highest growth rate) and we will investigate the evolution of this mode only.**

**In a bunch, the charge density *****n******b****** *****depends on the position *****z***** along the bunch and because the perturbation moves, its position *****z****** *****depends on *****t*****. **

**If *****n******b****** *****at the perturbation position changes slowly with *****t*****, the amplitude of the mode can is obtained as the solution of:**

**and using the previous results**

## For the case of a Gaussian bunch with rms length z the instability threshold is situated at the distance zT from the bunch peak:

**For the case of a Gaussian bunch with rms length ***********z***** the instability threshold is situated at the distance *****z******T***** from the bunch peak:**

- where* I* is the bunch current and *I**T* is the MBI current threshold.

**The perturbation typically originates at the bunch peak and then starts moving and growing exponentially, but when it arrives at a bunch position where *****n******b****** < *****than the MBI threshold***** *****the CSR wake cannot sustain the amplitude growth anymore and the modulation starts to decrease and is gradually reabsorbed by the bunch.**

**Using this result in the previous expression for the perturbation and considering that the radiated power is proportional to the square of the perturbation amplitude one finally finds:**

## The comparison of this simple model predictions with the ALS experimental data showed a good agreement up to a certain current (~19 mA).

**The comparison of this simple model predictions with the ALS experimental data showed a good agreement up to a certain current (~19 mA).**

**Above this value, the experimental points show a saturation effect that we think is due to the fact that at high currents, the MBI goes in the nonlinear regime before the perturbation arrives at the threshold point.**

- J.M.Byrd *et al*, PRL **97**, 074802, 2006

## The model can also account for the time structure shown by the CSR power signal in measured by the fast bolometer.

**The model can also account for the time structure shown by the CSR power signal in measured by the fast bolometer.**

** ****As previously said, the slicing seeds the perturbation that starts at the bunch peak, assumes its maximum amplitude at *****z******T*****, and after that is gradually reabsorbed. The CSR power radiated by the perturbation must show the same time structure, and the figure seems to confirm this scenario. **

**By calculating this value for our case, we estimate *****t******T ***** ~ ****31 ********s**** not far from the ****45 ********s**** of the figure. Apart from the accuracy of the model, we think that the discrepancy is also due to the fact that the signal in the figure was taken with a current higher than the ~ 19 mA at which the linear regime breaks.**

**In a more quantitative comparison, we can use the fact that the distance in time between the peaks of the two pulses in the bottom part of the figure should coincides with the value *****t******T****** ***** that takes for the perturbation for going from the bunch peak to the point *****z******T*****. **

## At the ALS we also tried to characterize the MBI power dependence on current using a different lattice with the momentum compaction reduced to about half its value (1.37 x 10-3)

**At the ALS we also tried to characterize the MBI power dependence on current using a different lattice with the momentum compaction reduced to about half its value (****1.37**** x ****10****-3****)**

**The exponential growth above the MBI threshold is still observed but it ****saturates much earlier**** than in the larger momentum compaction case.**

**As a consequence, we did not observe any measurable enhancement of the intensity of the CSR pulses induced by the slicing.**

## At saturation, the average power of the seeded CSR burst is about two orders of magnitude larger than for the “conventional” slicing case, but shows very large power fluctuations.

**At saturation, the average power of the seeded CSR burst is about two orders of magnitude larger than for the “conventional” slicing case, but shows very large power fluctuations.**
**Pump and probe and other experiments not requiring shot to shot intensity stability could benefit from this several orders of magnitude increase in power.**

**In a more speculative scenario, part of the THz signal could be brought back into the ring to co-propagate the bending magnet with a subsequent electron bunch, modulating its energy and seeding the MBI that generates a new burst that is then used in the loop for seeding a new fresh bunch. By this process, that continues involving all the bunches, one can in principle bring the CSR emission to a stable high power saturation regime where all the bunches radiate coherently.**
**Other FEL-like schemes exploiting the MBI gain are possible as well.**

**The graph shows how the 1 kHz power (synchronous with the laser) loses the quadratic dependence for currents above the MBI threshold.**

## CSR by Laser Slicing

**CSR by Laser Slicing**

**CSR from Seeded MBI:**** **

**K. Holldack *****et al.*****, PRL 96, 054801 (2006)**

**J.M.Byrd *****et al*****., PRL 96, 164801, (2006.)**

**K. Holldack *****et al.*****, PRST-AB 8, 040704 (2005).**

**S. Heifets, G. Stupakov PRST-AB 5, 054402, (2002)**

**S. Heifets and G. Stupakov, SLAC-PUB-11815, (2006)**

**J.M.Byrd *****et al*****, PRL 97, 074802, (2006)**

## In a slicing experiment, define the energy that a laser pulse at =852 nm must have in order to generate in an electron beam of 1.9 GeV an energy modulation six time larger of the beam relative energy spread. Assume that you are using a wiggler with parameter K=2. Assume also that the relative energy spread of the beam is 10-3 , that the laser pulse length is 50 fs (FWHM), and that the wiggler relative bandwidth is 1/NW (where NW is 50 and is the number of periods in the wiggler).

**In a slicing experiment, define the energy that a laser pulse at **********=852 nm must have in order to generate in an electron beam of 1.9 GeV an energy modulation six time larger of the beam relative energy spread. Assume that you are using a wiggler with parameter K=2. Assume also that the relative energy spread of the beam is 10****-3**** , that the laser pulse length is 50 fs (FWHM), and that the wiggler relative bandwidth is 1/N****W**** (where N****W**** is 50 and is the number of periods in the wiggler).**

**For a slicing experiment, list the system parameters that allows to control the CSR spectrum and explain their effect.**

**Calculate the growth rate and the perturbation velocity for the MBI mode with **********=6 mm for a beam in a storage ring with the following characteristics. Beam energy 1.5 GeV, momentum compaction  2,7 x 10****-3****, ring length 197 m, bending radius R=55m and particle density n****b****= 10****9**** electrons per cm. ********(3/2)~1.354.**

## From: http://physics.nist.gov

**From:**** ****http://physics.nist.gov**