C. Addi'onal FEL topics

Transcription

1 C. Addi'onal FEL topics

2 C. Addi'onal FEL topics C.1 Seeding schemes C.1.1 SASE C.2.2 Improvement of longitudinal coherence C.2 Schemes for increased output power C.3 Ultra- short X- ray pulses C.4 Crea'on of unusual X- rays

3 C. Addi'onal FEL topics C.1 Seeding schemes C.1.1 SASE C.2.2 Improvement of longitudinal coherence C.2 Schemes for increased output power C.3 Ultra- short X- ray pulses C.4 Crea'on of unusual X- rays

4 Self- amplified spontaneous emission (SASE) In the theore'cal treatment, it was always assume that there is a perfect plane E x wave of correct λ l available. In fact, there is not seed laser in the X- ray regime available. So how to we seed the FEL process? The most common solu'on is to use the spontaneous undulator radia'on as seed light (SASE). The problem is, however, that undulator radia'on (as ordinary ISR) origins from the random charge distribu'on in the electron bunch (Shot noise) and is therefore a random process. Hence the seed light is neither monochroma'c, nor transverse coherent nor longitudinal coherent. How much of a problem is that in fact.

5 Transverse coherence of X- rays from SASE Low- gain regime: The electron beam excites in the beginning not only the TEM 00. Several modes overlap and destroy the transverse coherence (no fixed transverse phase rela'on). High- gain regime: Since the TEM 00 is highest on axis, where the beam j z is largest, it grows faster then the other modes (mode cleaning). In the high- gain regime and in satura'on the TEM 00 mode is nearly purely present, which results in very high transverse coherence!

6 Longitudinal coherence of X- rays from SASE Light emission along the beam is a random process and hence there is no defined phase rela'on all along the electron beam. An appropriate model is the overlap of short coherent wave packages (also called longitudinal modes) that are shited by random phases. The average length of these individual wave packages is called coherence length and is given by < coh > p! = l 6 p 2 FEL r z L g0 Due to the phase shit jumps between the individual SASE radia'on, the X- ray radia'on will not be monochroma'c anymore. The spectrum is widened (see next page). Also shape of spectrum and the integrated X- ray power will fluctuate (stochas'c process).

7 Spectrum of SASE X- rays Longitudinal spectrum of the X- rays at the end of the undulator. A wider spectrum with width σ ω,av is made up by many spikes with width σ ω,spike. Proper2es of spectrum: The width of the spikes is related to full length of the photon beam!,spike 2p 2ln2 T bunch The width of the spectrum is related to the length of the longitudinal modes. The number of spikes is equal to the number of longitudinal modes M = T bunch coh P (Eph)(arb.units) x E ph (ev) x 10 4 The fluctua'ons of the integrated X- ray power vary strongly in the exponen'al gain regime (60-70%), but get reduced in the satura'on regime (20%).

8 SASE vs. seeded FEL simula'ons P [GW] CLIC15 SASE CLIC15 seeded z [m] GENESIS simula'ons with realis'c beam distribu'ons. 10kW laser used for seeding. About equivalent to SASE This already shows that a very strong seed laser is needed if SASE should be suppressed. SASE and seeded (steady state) simula'on give different results in satura'on regime. Reason is a that par'cles with detuned energy exist and have a high gain (see later more).

9 C. Addi'onal FEL topics C.1 Seeding schemes C.1.1 SASE C.2.2 Improvement of longitudinal coherence C.2 Schemes for increased output power C.3 Ultra- short X- ray pulses C.4 Crea'on of unusual X- rays

10 Concept 1: Higher harmonic genera'on (HHG) SASE FEL radia2on has several disadvantages: Widened bandwidth. Strong shot- to- shot fluctua'ons of the X- ray spectrum. Low longitudinal coherence. Strong X- ray power fluctua'ons in the exponen'al growth regime (less in satura'on). To improve the situa'on it would be preferable to seed the FEL processes with external longitudinal coherent light. On concept to create such seed light is to used higher harmonics of a laser: At SACLA, 'tanium- sapphire (Ti:Sa) laser was focused on Xenon gas cell where it generates higher order harmonics. FiTh harmonic (160nm) has been used to seed electron test beam. The smallest reached seeding wavelength has been 38nm demonstrated at FLASH (2013).

11 Concept 2: High- gain harmonic genera'on (HGHG) FEL is seeded with available laser at longer λ l In first low gain FEL (modulator), energy modula'on is created (only 'ny bunching). This energy modula'on is converted to a charge varia'on in a chicane (bunch compressor principle). A second high- gain FEL (radiator) is tuned to a higher order of the charge modula'on. If current modula'on at higher harmonic is strong enough to overcome SASE it can be used. Modula'on factor j i is reduced for higher harmonics.

12 Concept 3: Echo- enabled harmonic genera'on (EGHG) Idea is the same as for HGHG. Difference is that two modulators (and two lasers) are used to create a charge modula'on with stronger higher order components. First chicane over- compresses energy varia'on and second chicane acts as in HGHG. Result is a very spike charge modula'on. Therefore harmonics of a higher number (compared to HGHG) are s'll strong enough to seed FEL process. One problem is the adding up of energy spread in the modulators, which increases gain length.

13 Concept 4: Self- seeding This method does not rely on an external laser. The first undulator is operated in SASE mode for a few gain length. Then the created light is separated from the beam (chicane) and filtered my a diamond gra'ng monochromator crystal. The filtered light has much becer longitudinal coherence. In a second undulator, the filtered light is used as a seed for the same electron bunch. An addi'onal posi've effect is that the micro- bunching of the beam has been washed out in the chicane. This method can be used at any wavelength, but is limited by the performance of the diamond monochromator. The final spectrum is therefore broader than at HHG, HGHG or EEGH.

14 Overview of advanced seeding schemes FEL- Oscillator Direct seeding (HHG) High gain harmonic genera2on (HGHG) Echo- enabled harmonic genera2on (EEHG) Self seeding Light trapped in an oscillator. Limita'ons are mirrors. < 250 nm. Laser ionizes novel gases and creates higher harmonics. < 40 nm First seeding with laser (modulator). Then lasing at higher harmonic (radiator). < 10nm Complex three stage scheme similar to HGHG. < 1nm Interes'ng for sot XFEL design. Laser creates SASE light in first stage. Light is filtered. Second stage for lasing. No wave- length limita'on. Interes'ng for sot and hard XFEL design.

15 C. Addi'onal FEL topics C.1 Seeding schemes C.1.1 SASE C.2.2 Improvement of longitudinal coherence C.2 Schemes for increased output power C.3 Ultra- short X- ray pulses C.4 Crea'on of unusual X- rays

16 Energy detuning 1/2 P [GW] γ =0.0x10 3 γ =-0.2x10 3 γ =0.4x10 3 γ =1.00x10 3 γ =1.2x z [m] Assume seeded opera'on. Remember: seeding laser wave length determines wave length of X- rays (λ l = λ s ), since FEL acts as light amplifier. However, K u, λ u and γ determine the resonance wave length λ R of the FEL. Usually choice: λ R = λ s. But slight running detuned (via beam energy γ) increases the output power. Note also the unusual shape in the satura'on regime.

17 Energy detuning 2/2 From FEL theory the let gain curves have been derived. In the low gain regime (very small micro- bunching), no light amplifica'on for λ R = λ s. In high gain regime (strong micro- bunching) the maximum gain is close to λ R = λ s, but at slightly detuned. This also explains why SASE performs becer than a seeded FEL in terms of power. Some frequency components due to shot noise are detuned.

18 Tapering P [GW] % 0%, no de 20% 5% 2% 1% 0.5% % x 2 1% x z [m] If the undulator strength K(Z) is weakened along the FEL, the output power can be strongly increased. This is usually done by changing the gap size of the undulator. With a linear taper (star'ng at m) the power can be increase from 1GW to 30-40GW. With a quadra'c taper 50GW can be reached.

19 Tapering 2/ x γ [1] θ [ o ] Many papers claim tapering compensates for the energy loss of the beam. But this is only a small effect. More important is that micro- bunches are kept in the right have of the FEL bucket, where they transfer energy to the light wave. Tapering moves bucket to the let.

20 Circular polarized light and inverse tapering Nowadays mainly planar undulators in FELs (linear polarized light) User request also circular polarised light (helical undulator). An undulator variant for both types of polariza'on is a long planar undulator (easier to build) with a helical aterburner undulator. If linear polarised light is desired, jaws of helical undulator are opened and have no effect (only planar undulator). If circular polarized light is desired, the helical undulator is closed and, light will have a fast power rise due to the already bunched beam from the planar undulator. But then one gets a mixture or linearly and circular polarised light. The linear polarized light can be suppressed by an inverse taper of the planar undulator without destroying the bunching.

21 C. Addi'onal FEL topics C.1 Seeding schemes C.1.1 SASE C.2.2 Improvement of longitudinal coherence C.2 Schemes for increased output power C.3 Ultra- short X- ray pulses C.4 Crea'on of unusual X- rays

22 Mo'va'on Coulomb explosion: Photon beam ionizes probe and hence destroys it completely. Time scale is about 20-50fs. Usual FEL pulses are fs. Picture is smeared out. Ultra- short X- ray pulses: If the X- ray pulses can be made short enough (< 1-10fs) compared to the 'me scale of the Coulomb explosion, then an image can undisturbed image can be made. Also even fast processes can be 'me- resolved.

23 Overview of some concepts Short bunch mode By reducing bunch charge Q (20pC instead of 200pC), bunches can be made shorter 1-2fs. Gun laser already produces shorter bunches. Lower charge makes bunch compression easier. But lower average brilliance. Energy modula2on from laser Use laser together with beam in a modulator undulator to create a energy modula'on. Then inject electron bunch into undulator. Beam beam only lase were the energy is close to resonance. Due to the energy modula'on of beam, a series of very short pulses will be created. If the laser light only includes one op'cal period, a single spike can be created.

24 Emicance spoiling via foils Correla'on longitudinal and transverse plane (beam 'lted). The case in bunch compressors. Beam is passed through foil with slit. Emicance is only preserved at slit, but spoiled when passing the foil. Beam lases only where emicance is unspoiled.

25 C. Addi'onal FEL topics C.1 Seeding schemes C.1.1 SASE C.2.2 Improvement of longitudinal coherence C.2 Schemes for increased output power C.3 Ultra- short X- ray pulses C.4 Crea'on of unusual X- rays

26 Two- color FEL The availability of light of two different wavelength is demanded by the user community. This can be realised in different ways: Example 1: First SASE undulator is tuned to λ 1. The beam is moved through a chicane to wash out microbunching. Beam is injected into SASE undulator 2 with a different K to create light with λ 2. Here the light pulses are slightly separated in 'me. Example2: ATer first undulator light stays bunched and is injected in second undulator which is tuned in higher harmonic of bunching. Like this the two light pulses are on each other.

27 Applica'on of two color X- rays Performed at Elecra by K. C. Prince. Inten2on: measure the absorp'on edge more precisely (spectroscopy). Principle: Excite electrons with the two wavelength to two different states. The emiced photons from one state are an s- wave while the other state emits a p- wave. Each wave itself is symmetric is asymmetric but the overlap is not! By changing the rela've phase of the two X- ray wavelengths, the spa'al distribu'on of emiced light is changed. Experimental possibili2es: Very precise measurements of absorp'on edges are possible. The hope is to measure Wigner 'mes for the first 'me ('me delay of scacering events).

28 Summary The photon user community has in the order of members and FEL radia'on is highly demanded. The science performed at FELs is of highest impact and only a few users can be supplied at the moment. Therefore the field of free electron lasers is a very ac've research topic and of growing interest. FELs are a very interes'ng combina'on of the fields of beam physics, FEL science and photon science and there are many interes'ng and challenging problems to be solved. The University of Oslo is currently par'cipa'ng in a collabora've effort to make FELs cheaper and accessible to a wider user group. If you are interested in working on this subject (Bachelor, Master, PhD theses) please contact us!

29 Op'onal exercises You can solve the exercise with or without the hinds on the next page. Par2cle mo2on in an undulator: 1. Show that the average longitudinal par'cle speed can be approximated by v z (t) = p v 2 vx 2 1 c 1 1+ K rd order FEL equa2on: 2. Show that the solu'on of the 3 rd order equa'on has the following form, if space charge effect are negligible and the FEL process is on resonance. Ẽ x (z) =c 1 e (i+p 3) 2 + c2 e (i p 3) 2 + c3 e i 3. Show that for a seeded laser opera'on the coefficients c 1 = c 2 = c 3 = E in 3 with E in = Ẽx(z = 0) 4. Interpret the effect of the three different components of the solu'on Eq. (1) on the X- ray power in a qualita've way. How can the small- gain at the start of the process be explained from a sum of exponen'al func'ons.

30 Op'onal exercises (hinds) 1. The instantaneous speed v can be calculated from the γ factor of the par'cles. Then simplify the expression using Taylor expansion. Finally, use the expression for v x by differen'a'ng the known solu'on for x(t). 2. The made assump'ons correspond to k p = η b = 0. Use the Ansatz: Ẽ x (z) =Ae z 3. You will have to consider that the FEL process starts in the low- gain regime. 4. As a help, you can plot the real part of the terms individually for realis'c parameters to analyse their behaviour.