# Presentation: 580418

## Generating THz in Storage Rings.

**Part I**

**Fernando Sannibale**

## Coherent Synchrotron Radiation (CSR) has been matter of great interest and study in the last years:

** ****As a powerful diagnostic for bunch compressors in free electron lasers (FEL) (FLASH, LCLS, FERMI, ...);**

** ****As something to carefully avoid or at least control in every short bunch high charge accelerator where CSR can jeopardize the performances (linear colliders, short pulses synchrotron radiation sources, damping rings, ...);**

** ****But also as a ‘dream’ for potential revolutionary synchrotron radiation (SR) source in the THz frequency range;**

## Scarcity of broadband powerful source in such a region of the spectrum

**THz Science: ****collective excitations, protein motions **
**& dynamics, superconductor gaps, magnetic **
**resonances, terabit wireless, medical imaging, **
**security screening, detecting explosives & bio agents ...**

**1 THz **
**= 4.1 meV **
**= 33 cm****-1**
**= 300 ********m**

**“****DOE-NSF-NIH Workshop on Opportunities in THz Science” February 12-14, 2004**
**http://www.science.doe.gov/bes/reports/abstracts.html#THz**

##  High Stability

** ****Non interceptive radiation processes are required.**
**Synchrotron and edge radiation most efficient**

** ****Many users capability**

** ****Multicolor experiments capability**

** ****Capability of "exotic" experiments (femtoslicing, stacking, ...)**

##  Part II 

**CSR in storage rings by "short" bunches**

** ****Part II **

**CSR in storage rings: alternative schemes**

** ****Part I**

## The CSR factor g() determines the high frequency cutoff for CSR, while the vacuum chamber (shielding) defines the low frequency one.

**The CSR factor *****g*****(**********)**** determines the high frequency cutoff for CSR, while the vacuum chamber (shielding) defines the low frequency one.**

**The power spectrum of the radiation from a bunch with *****N***** particles is given by:**

## To extend the CSR spectrum towards higher frequencies

**To extend the CSR spectrum towards higher frequencies**
**the bunches must be shortened. **

## To extend the CSR spectrum towards higher frequencies: the ‘saw-tooth’ distribution is the best.

**To extend the CSR spectrum towards higher frequencies: the ‘saw-tooth’ distribution is the best.**

## Slide 9

## Shorten the bunches as much as possible.

**Find a mechanism for generating sharp edged distributions (saw-tooth like possibly).**

**And of course, put as much particles as possible in the bunch.**

**Extend the vacuum chamber cutoff towards wavelengths as long as possible.**

## Using the parallel plate model for representing the vacuum chamber effect for the case of synchrotron radiation from a bend, one can find the cutoff frequency:

**Using the parallel plate model for representing the vacuum chamber effect for the case of synchrotron radiation from a bend, one can find the cutoff frequency:**

**The radiation can be extracted from the vacuum chamber only if :**

**So, to extend the spectrum towards longer wavelengths ****large vacuum chamber gaps**** and ****small bending radius**** are required.**

## For a storage ring in the linear regime and for currents below the threshold for the microwave instability, the bunch is Gaussian with length:

**For a storage ring in the linear regime and for currents below the threshold for the microwave instability, the bunch is Gaussian with length:**

**So it is natural to try shortening the bunch using those knobs.**

**Unfortunately, we will see that for short bunches (~ ps) the situation becomes a little bit more complicated...**

## Wakefields:

**Wakefields:**
**CSR Impedance**
**Vacuum Chamber Impedance **

**Requires some current to be effective**

**And/Or**

## With a single frequency RF cavity with sufficient field amplitude, the potential well is with good approximation parabolic and the bunch is Gaussian at equilibrium.

**With a single frequency RF cavity with sufficient field amplitude, the potential well is with good approximation parabolic and the bunch is Gaussian at equilibrium.**

**In principle, by using additional high-harmonic cavities one could obtain more complex shapes for the potential well generating the non-Gaussian distributions we are interested to.**

**This is a very complex scheme to realize, and so far people has only added one higher harmonic cavity in rings. For this case:**

**Very difficult and not very efficient!**

## Wakefields:

**Wakefields:**
**CSR Impedance**
**Vacuum Chamber Impedance **

**Requires some current to be effective**

**And/Or**

## The single particle longitudinal dynamics in a storage ring is defined by the focusing strength of the RF cavity (ies) and by the lattice characteristics.

**We want to investigate if a non-linear momentum compaction can generate the strongly non-Gaussian distributions we are interested to.**

**The single particle longitudinal dynamics in a storage ring is defined by the focusing strength of the RF cavity (ies) and by the lattice characteristics.**

**The lattice component can be represented by the momentum compaction ***********C***** of the ring, defined by:**

**where *****L*****0**** is the ring length, **********  is the nominal energy in rest mass units, *****p*****0**** is the particle nominal momentum, and if ********** is the beam emittance:**

**The momentum compaction is a function of the lattice parameters and in the more general case can be a nonlinear function of the relative momentum difference:**

**where this relation defines the orbit length variation for an off-momentum particle.**

## But...

**The simulation is performed ****without damping****, and the figure shows the longitudinal phase space trajectories**

**Two stable "buckets" with different energy are clearly visible. **

**The bunch distribution is given by the projection of the phase space on the phase axis.**
**The figure shows perfect symmetry respect to the zero phase and so symmetric bunch distributions... **

**But...**

**Strongly nonlinear!**

## The synchrotron radiation losses break the symmetry of the phase plane and allow for asymmetric distributions.

**The synchrotron radiation losses break the symmetry of the phase plane and allow for asymmetric distributions.**

**But when the**** radiation damping is switched on****, the "centers" of the two buckets move to different synchronous phases for compensating for the ****different synchrotron radiation losses**** and the symmetry is broken!**

## The distribution moments show that even for this extreme case, the distribution is  only slightly asymmetric.

**The distribution moments show that even for this extreme case, the distribution is  only slightly asymmetric.**

## Wakefields:

**Wakefields:**
**CSR Impedance**
**Vacuum Chamber Impedance **

**Requires some current to be effective**

**And/Or**

## Because of the curved trajectory of the beam, the photons radiated from particles in the tail of the bunch catch up with the particles in the head.

**Because of the curved trajectory of the beam, the photons radiated from particles in the tail of the bunch catch up with the particles in the head.**

**The curved trajectory also allows for the electric field of these photons to assume a component parallel to the motion direction of the particles in the head and therefore to change their energy.**

## J.B. Murphy, S. Krinsky, R. Gluckstern , Particle Accelerators 57, 9 (1997)

- J.B. Murphy, S. Krinsky, R. Gluckstern , *Particle Accelerators ***57**, 9 (1997)

- Typical region
- of interest

##  = 4.35 m

**BESSY II case:   *****E***** = 1.7 GeV**

******** ****= 4.35 m**

***h***** = 1.75 cm**

- Tail

- Head

## where S(s) is the Step Function Wake

- and ***z*o is the natural bunch length.

**The current distribution *****I*****(*****s*****)**** can be**
**calculated by the Haissinski Equation:**

**The strongly nonlinear SR wake generates a distortion of the parabolic potential well due to the RF cavity, and the bunch assumes non-Gaussian equilibrium distributions. **

**The free space SR wake generates the saw-tooth like distributions we were looking for!**
- (Bane, Krinsky and Murphy AIP Proc. **367**,  1995)

## Slide 25

## The vacuum chamber shielding terms in the SR wakefield become negligible when:

**The vacuum chamber shielding terms in the SR wakefield become negligible when:**

** ****For a given bunch length ***********z*****, a proper choice of the bending radius **********  and of the vacuum chamber half-height *****h***** allows to make the shielding effects negligible.**

- J.B. Murphy, S. Krinsky, R. Gluckstern , *Particle Accelerators ***57**, 9 (1997)

## Long Range Resistive Wall wakefield (SI units - parallel plate model):

**For example: K. Bane, M. Sands "Micro Bunches Workshop" AIP Conf. Proceedings 367 (1995).**

**This wake can be added to the others in the calculation of the equilibrium distribution by the Haissinski equation. From the distribution the CSR factor and spectrum are then readily evaluated.**

**The example shows that the resistive wall can reduce the CSR intensity. In general larger gap (once more) and high conductivity chambers  are preferred.**

## The effect of the wake fields due to the vacuum chamber of an accelerator are usually modeled by using the broadband impedance model:

** ****The**** ****real (resistive) part**** ****of the impedance generates *****asymmetric non-Gaussian***** distributions and *****bunch lengthening*****. The *****bunch center of mass moves towards a different RF phase***** to compensate for the wake induced energy losses. **

** ****The**** ****imaginary (reactive) part**** ****of the impedance generates *****symmetric non-Gaussian***** bunch distributions. The bunch *****center of mass does not move***** (no energy losses). It generates *****bunch lengthening or shortening*****.**

**where the reactive  part can be either capacitive or inductive depending on the frequency.**

**In the short bunch regime of our interest, the effect of these wakes is usually negligible. **

##  Synchrotron Radiation Wakes Included (Free Space and shielded G1 and G2)

** ****Synchrotron Radiation Wakes Included (Free Space and shielded G1 and G2)**
** ****Long Range Resistive Wall Included**
** ****Coulomb Wake not Included (negligible)**
** ****Vacuum Chamber Geometric Wakes not Included (negligible)**

## The bunch distribution in a real ring is never completely smooth and shows a modulated profile that changes randomly with time (noise).

**The bunch distribution in a real ring is never completely smooth and shows a modulated profile that changes randomly with time (noise).**

**These micro-structures usually have characteristic length << than the bunch length and radiate CSR. The wakefield from this radiation modulates the energy of neighbor particles that starts to move inside the bunch due to the longitudinal dispersion of the accelerator. Part of these particles moves in the direction that increases the size of the radiating micro-structure, and thus increasing the CSR intensity creating a gain mechanism for the process . **

**Above a certain current threshold, this gain becomes large enough to sustain the micro-bunching process and to generate an exponential growth of the micro-structure amplitude (up to saturation in the non linear regime of the instability).**

**Such an instability, often referred as the**** ****micro-bunching instability (MBI)****, is nothing else that a SASE process in the THz regime.**

**The MBI, for the case of storage rings, was predicted by Sam Heifets and Gennady Stupakov (****PRST-AB 5, 054402, 2002****) and simulated by Marco Venturini and Bob Warnock (****PRL 89, 224802, 2002****)**

## Microbunching Model

- Simulation by Marco Venturini

**Small perturbations to the bunch density can be amplified by the interaction with the radiation. Instability occurs if growth rate is faster than decoherence from bunch energy spread. **

**Nonlinear effects cause the instability to saturate. Radiation damping damps the increased energy spread and bunch length, resulting in a pulsing ‘sawtooth’ instability. **

## In many electron storage rings around the world, strong random pulses (“bursts”) of CSR in the THz frequency range were observed for high single bunch current.

**In many electron storage rings around the world, strong random pulses (“bursts”) of CSR in the THz frequency range were observed for high single bunch current.**

**According to what said before, the presence of the micro-bunching instability should be associated with the emission of random "burst" of CSR.**

## The instability thresholds predicted by the Heifets-Stupakov model for the instability were in agreement with the measured thresholds

**The instability thresholds predicted by the Heifets-Stupakov model for the instability were in agreement with the measured thresholds**

**Experiments at the ALS provided the experimental confirmation that the THz CSR bursts were associated with the MBI.**

**The beam becomes unstable if the single bunch current is larger than (SI Units):**

## Bursting threshold

- BESSY II results: courtesy of G. Wuestefeld

- Agrees well with predicted microbunching thresholds

##  In 2002, The BESSY-II group provided the first evidence of stable CSR in a storage ring.

** ****In 2002, The BESSY-II group provided the first evidence of stable CSR in a storage ring.**
**Abo-Bakr *****et al.*****, PRL 88, 254801 (2002),  **
**and ****M. Abo-Bakr *****et al*****., Phys. Rev. Lett. 90, 094801 (2003)**

**Very interesting characteristics of the BESSY results were:**
** ****a very stable CSR flux (no presence of bursts), **
** ****an impressive power radiated in the THz region,**
** ****and a spectrum significantly broader than the one expected for a Gaussian distribution their bunch length.**

## The understanding of the physics behind the BESSY results showed the dominant role played in the short bunch regime by the SR wake and allowed to develop a model for optimizing a storage ring as a stable source of THz CSR.

**The understanding of the physics behind the BESSY results showed the dominant role played in the short bunch regime by the SR wake and allowed to develop a model for optimizing a storage ring as a **_**stable**_** source of THz CSR.**

**Such a model has been used for calculating the CSR performance of a number of existing storage rings (DA********NE, Bates, SPEAR, ...)  and also for designing a storage ring completely optimized for the generation of stable CSR in the THz frequency range (CIRCE, later in the lecture).**

**The figure shows the model predictions compared to the BESSY II data.**
**Shielding and resistive wall contributions were included.**
**The "width" of the model predictions accounts for the indeterminacy on the knowledge of the BSSY II machine parameters.**

- (F. Sannibale *et al*., PRL **93**, 094801, 2004.)

## We now have all the information required for optimizing a storage ring as a source of stable CSR in the THz frequency range. We learned that:

**We now have all the information required for optimizing a storage ring as a source of stable CSR in the THz frequency range. We learned that:**

** ****Shielding effects due to the vacuum chamber need to be carefully minimized****. A criterion was given that showed that by using a large gap vacuum chamber and a small bending radius the shielding can be made negligible.**

** ****Resistive wall impedance needs to be minimized****. A large gap-high conductivity vacuum chamber makes the effect negligible. The "geometric" vacuum chamber impedance has usually a very small effect in the short bunch regime.**

** ****The spectral bandwidth of the CSR is determined by the bunch length and longitudinal distribution****. Short asymmetric equilibrium distributions with a sharp edge generated by the SR wakefield significantly extend the bandwidth.**

** ****The maximum current per bunch is limited by the MBI****. In order to obtain a stable CSR emission, the current per bunch must be maintained below the instability threshold.**

**In what follows, we will make the (realistic) assumption of a storage ring where the vacuum chamber has been properly designed in order to make the shielding and vacuum chamber impedance effects negligible. For such a ring only the**** free space synchrotron radiation wakefield ****needs to be considered.**

**We also assume linear RF focusing.**

## The factor F is proportional to the distribution integral.

- K. Bane, S. Krinsky, J.B. Murphy, *Microbunches Workshop, *Upton NY 1995

**The factor *****F***** is proportional to the distribution integral.**
***F*****  also indicates the bunch distortion: the larger the more distorted is the bunch.**

*E* = beam energy
_*B *__= dipole field in the bending magnet_
*f**RF* = RF frequency
*V**RF*= peak RF voltage
***z*0 = Natural bunch length

**The Haissinski equation for the free space SR case assumes the shape:**

**Free Space SR Step Function Response**
**(wake function of a unit step - SI units)**

**The figure shows an example of equilibrium distributions obtained by solving this equation, and from them the number of particles per bunch is derived: **

## We already saw that the MBI sets a limit to the maximum current per bunch. This limit can be written as: 

**We already saw that the MBI sets a limit to the maximum current per bunch. This limit can be written as: **

**we obtain the stability condition:**

**And by comparing *****N******S***** with the number of particles per bunch that we previously calculated **

**Experimental results at ALS and at BESSY II have shown that the first unstable mode for the MBI shows up when ********** ~ ***********z*****0**

## We can now calculate the maximum stable distribution distortion for F = FMAX and from that the CSR form factor g() for this case:

**The last equation shows that CSR form factor is fully defined by the choice of the natural bunch length ***********z*****0****:**

** ****We already showed that the low frequency roll-off is instead defined by the vacuum chamber cutoff**

## Using the last expression, the one for NMAX, and assuming Nb bunches we obtain the maximum power radiated by a storage ring.

**For synchrotron radiation and for wavelengths much longer than the critical wavelength, the power radiated by a single electron in a ring with length *****L*****, is given by:**

## The momentum compaction does not appear among the above parameters but plays a fundamental role. It is used for maintaining z0 constant while freely changing the other quantities.

**The design of an optimized CSR THz source**** ****should probably start by deciding the desired bandwidth for the coherent radiation.**

**We saw how this choice imposes constraints on the vacuum chamber gap and on the dipole bending radius (low frequency cutoff) and also ****imposes the value for the natural bunch length ***********z*****0**** (high frequency cutoff).**

**The total power radiated within the selected coherent bandwidth can be maximized by the proper choice of the machine parameters according to:**

**The selection of ***********z*****0**** allows also to define the vacuum chamber characteristics necessary to make the effect of shielding and of resistive wall and geometric wakefields negligible. **

## ...

**poor lifetime, increased sensitivity to instabilities, .... **
**And also because the dependency of the CSR Power on the energy is weak.**

**In a small ring straight sections are short. Reasonably long straight sections allow interesting upgrades using insertion devices.**
**Additionally, the control of the machine parameters, is extremely important for the CSR tuning. Space for several families of quadrupoles and sextupoles is required**

**Extreme maximization of *****B***** and *****V******RF***** requires **
**superconductive systems with high cost impact **

**...**

## Very large divergence! The beamlines must be designed with very large acceptance to efficiently extract the radiation and to avoid undesired interference issues.

**Very large divergence****! The beamlines must be designed with ****very large acceptance**** to efficiently extract the radiation and to avoid undesired interference issues.**

## Edge radiation allows for smaller acceptance beamlines.

**Edge radiation allows for smaller acceptance beamlines.**

**ESRF,**
**ANKA,**
**SOLEIL**

## DBA with Control up to 3rd order C

**10****6**** - 10****8**** power gain with respect to**
** ****the ALS BL 1.4 at the maximum current!**

**L= 66 m**
**Normal Conductive RF**
**Normal Conductive Dipoles**
**DBA with Control up to 3****rd**** order ********C**

## Horizontal Acceptance = 300 mrad

**Power integrated between 1 and 100 cm****-1 **

|  | rms pulse length
[ps] | Total power
[w] | Pulse peak power 
[kw] | Energy per pulse
[nJ] | Total current
[mA] | Current per bunch
[A] | Particles per bunch | Momentum
Compaction |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Mode 1 | 1.0 | 2.04 | 0.54 | 1.36 | 8.0 | 24.0 | 3.3 107
 | 2.4 10-4 |
| Mode 2 | 2.0 | 15.1 | 2.0 | 10.0 | 35 | 106 | 1.5 108
 | 8.6 10-4 |
| Mode 3 | 3.0 | 47.8 | 4.3 | 32.0 | 90 | 272 | 3.7 108
 | 1.9 10-3 |

*E* = 600 MeV	*f**RF* = 1.5 GHz
*V**RF* = 0.6 MV	*L* = 66 m
*h* = 330		**= 1.335 m

**- Currents increase a factor 2.5 **

## CIRCE Parameters (NC RF):

- _CIRCE Parameters (NC RF):_
*E* = 600 MeV	       *f**RF*  = 1.5 GHz
*V**RF* = 0.6 MV	       *U*0 = 8.62 kV
*I**total* = 8-90 mA	       *I**bunch* = 24-270 A
*L* = 66 m	       *# buckets* = 330
****= 1-3 ps	     ****= 4.5  10-4
- = 2  10-3 - 2  10-4     ** = 1.335 m
- 2h = 4 cm	       = 0.06 - 0.18

** ****Periodicity = 6**
** ****DBA lattice 50 nm emittance (diffraction limited in far-infrared)**
** ****Variable momentum compaction with 3rd order correction**
** ****Magnets pre-aligned on girders**
** ****Shielding fits directly over magnets (i.e. no tunnel access)**

- _CIRCE Parameters (SC RF):_
- Same as the normal conductive case but:
*V**RF* = 1.5 MV
*I**total* = 20-225 mA	       *I**bunch* = 60-675 A
**= 10-2 - 10-3

##  All Magnets Designed 

** ****All Magnets Designed **

** ****Built Prototype of the (very!) large acceptance (300 x 140 mrad****2****) dipole vacuum chamber**
** ****Performed RF Measurements**
**for High Order Modes (HOM)**
** ****Defined Efficient Scheme**
**for HOM Damping**

## Microbunching instability (MBI):

**Microbunching instability (MBI):**
-  Sam Heifets and Gennady Stupakov, PRST-AB **5**, 054402, 2002
-  Marco Venturini and Bob Warnock, PRL **89**, 224802, 2002
-  J.M.Byrd *et al*., PRL **89**, 224801, 2002

**Stable CSR Model:**** **
-  K. Bane, S. Krinsky, J.B. Murphy, *Microbunches Workshop, *Upton NY 1995 AIP 	Proc. **367**,  1995.
-  F. Sannibale *et al*., PRL **93**, 094801, 2004.
-  F. Sannibale *et al*., ICFA Beam Dynamics-Newsletter **35**, 2004

**CIRCE:**
-  J. M. Byrd, *et al*., Infrared Physics & Technology **45** (2004) 325-330.
-  J. Byrd, *et al*., 9th European Particle Accelerator Conference, Lucerne, 	Switzerland, July 2004. LBNL-55603.

**CSR in Storage Rings: ICFA Beam Dynamics-Newsletter 35, 2004**
**(http://icfa-usa.jlab.org/archive/newsletter.shtml)**

## Assuming that you need a storage ring-based CSR THz source with a given spectrum, calculate a set of parameters that maximizes the radiated power within the desired bandwidth. Explain the reasons behind your choices.

**Assuming that you need a storage ring-based CSR THz source with a given spectrum, calculate a set of parameters that maximizes the radiated power within the desired bandwidth. Explain the reasons behind your choices.**

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

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