A simple method for a very short X-ray pulse production and attosecond diagnostic at LCLS

Accepted Manuscript A simple method for a very short X-ray pulse production and attosecond diagnostic at LCLS Alexander Novokhatski, Dorian Bohler, Axel Brachmann, William Colocho, Franz-Josef Decker, Alan S. Fisher, Marc Guetg, Richard Iverson, Patrick Krejcik, Jacek Krzywinski, Alberto Lutman, Timothy Maxwell, Michael Sullivan

PII: DOI: Reference:

S0168-9002(18)31814-X https://doi.org/10.1016/j.nima.2018.12.017 NIMA 61702

To appear in:

Nuclear Inst. and Methods in Physics Research, A

Received date : 3 July 2018 Revised date : 30 November 2018 Accepted date : 5 December 2018 Please cite this article as: A. Novokhatski, D. Bohler, A. Brachmann et al., A simple method for a very short X-ray pulse production and attosecond diagnostic at LCLS, Nuclear Inst. and Methods in Physics Research, A (2018), https://doi.org/10.1016/j.nima.2018.12.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

*Manuscript Click here to view linked References

A SIMPLE METHOD FOR A VERY SHORT X-RAY PULSE PRODUCTION AND ATTOSECOND DIAGNOSTIC AT LCLS Alexander Novokhatski *, Dorian Bohler, Axel Brachmann, William Colocho, Franz-Josef Decker, Alan S. Fisher, Marc Guetg, Richard Iverson, Patrick Krejcik, Jacek Krzywinski, Alberto Lutman, Timothy Maxwell and Michael Sullivan. SLAC National Accelerator Laboratory, Menlo Park, California, USA Abstract We discuss how by using the wake fields generating in a corrugating plate we may increase the resolution of a transverse diagnostic cavity while producing an extremely short X-ray pulse at LCLS.

INTRODUCTION To measure the time profile of an electron beam usually an old television set video (TV) type technique is used. In a vacuum TV tube a beam particle while passing between two electrodes gets a kick in a horizontal direction from the electric field applied to these electrodes. After that the particles travels to the phosphorescent screen. If the kick changes in time then the beam particles will touch the screen at different horizontal position. If the kick is linear increasing in time, then the position of the beam particles will be also linear. The intensity of the light from the spot, which is touched by the electrons, is proportional to the number of these electrons. Measuring the intensity of the light from the screen we can find the temporal profile of the electron beam. Naturally the voltage must be synchronized with a beam. This method is also used in the streak cameras for the electron beam, which is converted from the measured light pulse. To resolve shorter electron bunches we need a higher sweeping speed. Today the resolution of the modern streak cameras is better than 1 ps [1]. During this time a light can pass a distance of 300 micron. To achieve better resolution people use a transverse mode in the RF cavity. The sweeping speed determines by RF power and mode frequency. Higher frequency leads to better resolution. In the reference [2] the authors proposed an idea for a streak camera whose time resolution is lower than 100 fs. The method replaces the high-voltage sweep component of a conventional streak camera by a TM110-mode RF cavity, which performs a transverse circular sweep of the electron bunch in the streak tube through a rotating magnetic field. The proposed method also allows one to overcome the problem of triggering, which is a serious limitation of conventional streak cameras. Several transverse cavities at S-band and X-bands frequencies were built for the beam and X-ray diagnostic at Free Electron Lasers [3-4]. The X-band transverse cavity at LCLS allows achieving resolution of up to several femtoseconds [5]. The light can pass a dis___________________________________________

* [email protected]

tance of 0.3 micron during the time of 1 fs. In this paper we demonstrate how to make a further step to attosecond range of resolution. During the time of 100 as the light advances a mere 0.03 micron or 300 angstroms, comparable with the Extreme Ultraviolet (EUV) wavelength. This may be very attractive for study of the attosecond physics at the nanoscale [6]. Recently a new device, which is called a “RadiaBeam/SLAC dechirper” was installed at LCLS. The main goal of this device was to compensate energy chirp of a bunch, which is needed in previous stages for the bunch temporal compression [7]. Similar idea of using wake fields to produce an energy chirp in a bunch was suggested many years ago with an application for a storage ring [8]. However, at the LCLS the energy chirp in a bunch is not large, so the dechirper found other applications, mainly as a kicker. A possible application was to use it as a passive deflector for measuring the length of very short bunches, less than 1 fs [9,10]. Of cause the idea of using a passive device like an active device is not new. Usually a passive device is optimized for a single frequency and excited by a train of bunches. For example, the excitation of the passive cavity in a klystron by previous bunches establishes the amplitude and a phase of the field acting on subsequent ones. The same principle must work for a single bunch. When a bunch travels near a corrugated plate (Fig. 1), each particle gets a transverse kick depending on its position in the bunch. The tail particles get more kick.

Figure 1: A fragment of a corrugated plate of the RadiaBeam/SLAC dechirper. The red line shows a bunch trajectory. The transverse force also depends nonlinearly on the transverse position. The stretched bunch has been measured at the YAG screen 100 m downstream of the dechirper. The most important aspect of this measurement is that that no synchronization is needed. The Green’s

function for the transverse kick was evaluated based on precise wake field calculations for the dechirper’s corrugated structure [9] using the same calculation method as for coherent synchrotron radiation (CSR), code “NOVO” [11]. Using Green’s function we can recover the longitudinal shape of the bunch. Recent measurement using wire scanners showed that the kick from the dechirper can be strong enough to stretch a short bunch. However, we found another possibility to measure short bunches together with the LCLS X-band transverse cavity [4-5], increasing in this way the resolution of the RF deflector and at the same time we can produce very short X-ray pulses. This method in general is very similar to a fresh slice technique [12], but much easier to use. It is not required to measure the orbit in the undulator line for correcting the bunch trajectory right after the dechirper [12]. In the first chapter we describe the details of the transverse kick from the wake fields excited by a bunch passing by a corrugated plate. It is worth to be mentioned that a similar analyses of the surface wake fields was carried out for a high frequency accelerating structure [13-16]. We present also the comparison of calculations and measurement. In the next chapter we describe the possibility to measure the beam profile at the YAG screen 100 m downstream the dechirper. And in the final two chapters we describe the simple technique to produce very short X-ray pulses while increasing the resolution of the RF deflector. Also primary experimental results will be presented.

traveling along the linear accelerator. The bunch “head” is on the left side in Fig. 2. And the bunch “tail” is on the right. We can call the second horn as a bunch “tail”. The bunch trajectory distance to the jaw is 150 µm, the bunch charge is 175 pC, and the beam energy is 13.3 GeV. The direction of the kick is towards to the corrugated plate (jaw) that means jaw attracts the bunch. The dependence of the kick is nonlinear along the bunch length, but in the region of the bunch “tail” it is almost liner with a position. It can be seen that maximum value of the kick is high enough, comparable with a strong magnetic corrector of the strength of 0.11 kG m.

TRANSVERSE KICK FROM A CORRUGATED PLATE

It is important to note that when a particle in the bunch is kicked by the transverse wake field; it also decelerated by a longitudinal wake field. Figure 3 shows the particle energy loss as a function of the particle position in the bunch. The dependence of the longitudinal losses is also nonlinear with the particle position, but in the bunch “tail” region it reaches the maximum value and is almost flat.

Here we analyse the transverse kick of the wake field generated by a beam passing by the corrugated plate of the Radia-Beam/SLAC dechirper. The practical design of the dechirper [17] consists of two identical movable parallel plates (jaws) with corrugated walls in the form of a periodic set of planar ridges, as shown in Fig. 1. In the horizontal dechirper the ridges are oriented in the vertical direction. The period of corrugations is 0.5 mm; the thickness of a ridge is a half of a period. The transverse sizes of a ridge are: height is 0.5 mm and length is 12 mm. Both jaws can be moved independently. The total length of a corrugated plate is 2 m. There are two dechirpers were installed. The vertical dechirper has horizontal jaw faces and moves vertically and the horizontal dechirper has vertical jaw faces and moves horizontally. In our proposed method we use the corrugated plats of the horizontal dechirper to deflect the beam. Precise numerical calculations of the wake fields for the case when a bunch travels very close to one jaw showed that the kick for a tail particle can be so large that we can resolve the bunch structure at very small time intervals even for high energy beams [9]. An example of a relative kick function along a 50-fs (FWHM) bunch with two horns (due to bunch compression) is shown in Fig. 2. The bunch shape was taken from a measured distribution. A bunch assumes a double horn shape after the second bunch compressor due to wake fields excited by a bunch

Figure 2: A bunch shape (blue line) and the corresponding transverse kick along the bunch (red line). The bunch “head” is on the left and the bunch “tail” is on the right. The distance from the bunch to the jaw edge is of 150 micron.

Figure 3: A bunch shape (blue line) and the corresponding energy loss along the bunch (red line). The bunch “head” is on the left and the bunch “tail” is on the right. We also show a plot of the particle energy loss as a function of the transverse kick in Figure 4 for different distances  between the beam trajectory and corrugated plate. There are regions in the vicinity of the bunch “tail” where energy loss does not change much. At the distance

of   0.15 mm the energy loss is flat for the transverse kick of 250 rad to 320 rad.

Figure 4: A particle energy loss as a function of the transverse kick acting on this particle. We compared wake field calculations with the measured transverse positions of a bunch at the first downstream beam-position monitor (BPM). This BPM is located at the distance of 16.2 m to the center of the corrugated plate of the horizontal dechirper. There are three correctors and one defocusing quad between a horizontal dechirper and the BPM. The beam is usually steered in the dechirper region, so correctors are almost zeroed. But the defocusing quad, which is 1.5 m upstream of the BPM must be taking into account. It produces additional kick of order of 5-10%. While measuring the horizontal displacement at the BPM we include the defocusing quad. Naturally a BPM can show only the average kick of the bunch, which is a convolution of the particle kick and bunch distribution. When the beam is steered in dechirper region the corrugated plates are aligned to be parallel to the beam. Based on the jaw alignment and calibration of the position we may assume that we know its position with accuracy of ±10 micron. The bunch charge was 175 pC and beam energy was 13.3 GeV. The result of the averaged bunch kick is shown in Fig. 5 as a function of the distance between the bunch trajectory and the jaw edge. Black diamonds shows measured horizontal kick with a stochastic error. Red line shows the calculated horizontal kick.

Figure 5: Measured averaged transverse kick of a bunch passing by 2 m long corrugated plate at different distances. Bunch charge is 175 pC, beam energy is 13.3 GeV. Numerical result is shown by a red line.

Averaged values and errors were calculated using 50 shots for each position of the jaw. Systematic errors due to intimal displacement of the beam at the BPM are subtracted and effect of a defocusing quad is taken into account. We can see a close agreement with the numerical calculations, which were done long before the measurements. The kick increases strongly when the beam trajectory approaches the jaw face. A power approximation of the measured kick gives the increment of -2.5. We also made measurement of the bunch energy loss using the vertical dump magnet and downstream BPMs, where vertical dispersion function is large. The incoming energy jitter was measured at the beginning of LTU by BPMs and was subtracted. This is the same technic, which was used to measure the wake fields losses in the 400 m long region from the linear accelerator to undulators (LTU) [18]. The measured energy loss result is shown in Fig. 6. Black diamonds shows measured energy loss with a stochastic error. Red line shows the calculated energy loss. Here we can also see a close agreement between calculations and measurements. One can compare the presented results of measurements with the previously published (Ref. [19]), which were matched to some analytical model and did not take into account the effect of the defocusing quad before a BPM.

Figure 6: Measured averaged energy loss of a bunch passing by a corrugated plate at different distances. Bunch charge is 175 pC, beam energy is 13.3 GeV. Numerical result is shown by a red line. The field, which generated by a bunch passing a corrugated plate is a nonlinear function of the transverse coordinates. Fig. 7 shows the distribution of the horizontal kick relative to a bunch horizontal position at the longitudinal coordinate of the “tail” of a bunch. A green line shows the kick when the distance between the bunch trajectory and the jaw edge is 250 micron. A blue line shows the same for 200 micron and a red line for 150 micron. The transverse bunch shape is a delta function of horizontal and vertical coordinates.

Figure 7: Distributions of the horizontal kick acting at the longitudinal coordinate of the bunch “tail“ along the horizontal direction relative to a bunch horizontal position. A green line shows the kick when the distance between the bunch trajectory and the jaw edge is 250 micron. A blue line shows the same for 200 micron and a red line for 150 micron. It can be seen from the plot that a particle, which can have a horizontal position closer to the jaw edge gets a much more kick and a particle, which is far away gets less kick. This is a defocusing part of the kick. The defocusing action at the longitudinal position of the bunch “tail” is so strong that a particle with a horizontal displacement of 50 micron from the bunch position in the direction to the jaw will get a kick of 50% higher in comparison with a kick, which a particle gets inside the bunch. And a particle with the same displacement but in the opposite direction (opposite to the jaw) will get a kick of 30% less. The difference in numbers tell us that for small distances to the jaw (<250) we need to take into account higher nonlinear kick harmonics. The vertical kick in the case of vertical corrugated plates is zero inside the bunch, but has a gradient that means a focusing force. The distribution of the vertical kick along the vertical coordinate relative to a vertical bunch position is shown in Fig. 8 for different distances of the bunch trajectory to the jaw. Vertical kick is calculated for a particle, which has a longitudinal position of the bunch “tail”. The transverse bunch shape is a delta function of horizontal and vertical coordinates.

Figure 8: Distribution of the vertical kick acting at the longitudinal position of the bunch “tail” along the vertical direction relative to a bunch vertical position for different distances of the bunch trajectory to the jaw edge. It can be seen from Fig. 7 and Fig. 8 that additionally to the horizontal kick and energy loss, a particle of the bunch of the finite transverse sizes will get a nonlinear defocusing force in the horizontal direction and a nonlinear focusing force in the vertical direction. To calculate forces acting inside a bunch with finite transverse sizes we can use previous results. Horizontal kick Fx  s, , x  acting on bunch particle with a horizontal coordinate x relative to a bunch horizontal position  and a longitudinal position s is a convolution of a bunch

horizontal

distribution

 x  x  and a kick

f x  s, , x  from a bunch with a delta function shape (Fig. 7) 



Fx ( s, , x)     f x  s,    , x    d  

(1) Vertical kick is convolution of a bunch vertical distribution and a kick from a bunch with a delta function shape (Fig. 8) 

Fy ( s, , y ) 



y

  f y  s, , y    d

(2)



We can compare this focusing-defocusing action with an electromagnetic quad. For a 50 micron bunch in horizontal and vertical directions it will be equivalent to a quad with a strength of 600 kG for a distance of 150 micron between the bunch trajectory and the jaw edge. It will be difficult to compensate this focusing-defocusing effect with usual linac quads. Images with over focused bunches will be shown in the next chapter. However for lager distances like 250 micron the equivalent strength of a quad is six times smaller and become comparable with a focusing quad, which is situated right upstream the horizontal dechirper. If we can increase the focusing effect from this quad then we can make a smaller beam size in

the dechirper and compensate the focusing effect after the dechirper. For some applications we can use an approximate presentation of the kick, which includes value at the bunch position and its derivate (gradients) in horizontal and vertical directions. Calculated results for the gradient of the transverse forces along the bunch are shown in Fig. 9 for the distance from the bunch to the jaw edge of 150 micron. A red line shows a strong focusing force in the vertical direction. A green line shows a strong defocusing force in the horizontal direction and a blue line shows the bunch shape.

K1,2 ( s,  ) 

s   Q g1,2  s  s ',     0 ( s ', x, y )dxdy  ds ' (5)  P0    

The kick is normalized to the longitudinal momentum P0 . The Green's functions g1,2 ( s,  ) were evaluated from the previously presented wake field calculations. With this approach we ignore higher order nonlinearities. With the wake field deflection, a bunch assumes a special shape: streaked and defocuses in one direction and focused in the other. Assuming that motions in horizontal and vertical dimensions are independent we can calculate the horizontal bunch distribution using a Gaussian bunch distribution at the corrugated plate ple linear lattice:

 scr ( xscr ,  ) 

0  s, x.x

and a sim-

 

    s, x, x dx ds 0

scr

 

(6) 0   x   m11 m12  xscr        K s, , x      m   x   21 m22   xscr    Here x' is the relative particle horizontal momentum and mik = aik−1 is an element of the inverse transfer matrix from the dechirper to the screen: Figure 9: Gradient of the transverse force along the bunch: strong focusing force in the vertical direction (red line) and strong defocusing force in the horizontal direction (green line). A blue line shows the bunch shape. The distance from the bunch to the jaw edge is of 150 micron. This focusing effect of the wake fields has been used to control the lasing slice of an FEL in a matching-based fresh-slice scheme [20]

IMAGE OF A DEFLECED BUNCH ON THE SCREEN As we mentioned before we intend to measure the profile of a stretched bunch at the YAG screen 100 m downstream of the dechirper. To describe a shape of a bunch at the screen we can assume that a horizontal kick K ( s, , x) acting on a particle from a vertical corrugated plate consists of two functions. First one K1 ( s,  ) is a transverse kick acting in a middle of a bunch at the longitudinal position s when a bunch is displaced relative to the corrugated plate at the distance  . Second function K 2, X ( s,  ) is an x-derivative

K  s, , x   K1  s,    K2  s,   x   

(3)

Vertical kick has only a focusing force

K  s, , y   K2  s,   ( y  y0 )

(7) Integration over x' can be done only after determining the matrix elements. The lattice is optimal when αdech = 0 at the dechirper and the phase advance to the screen Δψ = 90°, and so we get:

 0   aik    1    dech  scr 

 dech  scr    dech   scr  scr 

  dech   scr  scr  mik    1     dech scr 

   dech  scr     0  

Functions K1,2 are integral convolutions of the bunch

(8)

and

(9) We may assume that the distribution in x and x' has a Gaussian shape. In this case we can integrate over x' analytically. The bunch size at the screen without deflection will be determined by the bunch emittance:

(4)

y0 is the center of mass position in the vertical direction. charge distribution and Green’s function g1,2 ( s,  )

 xscr   a11 a12   x         xscr   a21 a22   x    x   m11 m12   xscr          m  x   21 m22   xscr 



2 scr



 xdech 2 21

m

2

  xdech  dech  scr   scr 2

(10)

To recover the initial longitudinal bunch distribution

 ( s) 





0

( s ', x )dx

(11)



using the image on the screen, we need to solve the integral equation of the first order:

 scr ( xscr ,  ) 



   s, x  ds 0

(12)



It is not a simple problem, mainly because of the “head” of the bunch, which does not get any kick; however, the “tail” of the bunch gets almost linear kick as we showed before and can be much easily reconstructed. A possibility to do the reconstruct is also discussed in Ref. [21-23]. We can better compare predicted from Eq. (4) distributions on the screen and measured distributions assuming that initial bunch shape, upstream the corrugated plate, is a Gaussian distribution. It happens that the initial measurement of the profile of the beam deflected by the wake fields excited in the horizontal dechirper was done not using YAG screen, but a wire scanner situated not very far from the screen. Figure 10 shows the beam profile when the distance between the beam trajectory and dechirper jaw edge is 410 µm. Blue dots are measured points, and a red line shows an analytical solution from Eq. (4). The bunch “head” is on the right of the plot and the bunch ”tail” is on the left.

Figure 10: Beam profile measured by a wire scanner (blue dots). A red line shows an analytical profile derived from Eq. (6). The amplitude of the calculated profile and some lattice parameters were adjusted to optimize the fit, but were then fixed and used for other profiles. One can see a good agreement. Main change of the beam profile due to the wake field kick is on the left side of distribution while the right is keeping initial profile. However from this distribution is it difficult to see that the beam profile has two horns. Much better results can be achieved with a stronger kick. Figure 11 shows the change in the beam profile, measured by the wire scanner, as the distance between the bunch trajectory and the jaw edge becomes smaller: the screen distribution increasingly approaches the shape of the initial distribution of the bunch (compare the red line of Fig. 11 to the blue line of Fig. 2).

Figure 11: Measured beam profile at different distances between the beam and the dechirper edge, and the corresponding analytical profiles. A 50-fs bunch stretches to a length of 0.6 mm at the wire scanner when the distance from the beam to the dechirper face is 330 µm. Theoretically, if can make a small transverse beam size of order of 10  in the dechirper region, then we can move the jaw closer to the beam (=60 µ) resulting in increasing of the kick more than 60 times. At this condition we can get a resolution of less than 1 fs. A beam profile monitor (YAG screen) shows a two dimensional shape of a deflected bunch. Typical shapes are shown in Fig. 12 for different distances from the bunch trajectory to the jaw.

Figure 12: Images of the deflected bunch on the YAG screen for different distances between the bunch trajectory and the jaw edge. In experiment it is not so easy to make a small distance between a bunch trajectory and the jaw edge. Mainly, because of the beam aborts due to radiation caused by a particle loss in the beam line. More details can be seen in three dimensional presentation of the 2-D plot from the screen. An example for distance of 0.3 mm between the bunch trajectory and the jaw edge is shown in Fig. 13. We can see clearly the shape of the bunch “tail”, which is on the left and a strong focusing of the “tail” in the vertical direction. For shorter distances (compare with Fig. 12) the focusing effect become much stronger and even over focus the “tail”.

which right downstream the horizontal dechirper. This measurement is similar to X-ray pulse energy measurement but using corrector in the undulator region. The result of our measurement is shown in Fig.14. It can be seen that to decrease the X-ray pulse energy twice we need only ± 0.0018 kGm change of the corrector magnetic field. This is equal to an angle of 4.5 μrad. Now we zoom in out a plot from Fig. 2, compensate the wake field kick with a corrector and measure the time spots corresponding to the angle limits. Figure 15 presents this procedure: a red line shows a kick near the compensating point, dotted black horizontal lines show the angle limits and vertical green lines show the time interval for X-ray production. Bunch shape (the “tail”) is shown by a blue line.

Figure 13: Tree dimensional presentation of the deflected bunch on the YAG screen. The bunch “tail“ is on the left.

VERY SHORT X-RAY PRODUCTION The main idea to produce ultra-short X-ray pulses is to use wake field to kick to the bunch and then compensate the kick of the bunch “tail” with a corrector. Existing LCLS lattice includes a horizontal corrector, which is situated immediately after the horizontal dechirper. If the “tail” produced X-rays without wake field kick before, then with a compensated kick it will propagate to undulators region in the same way and produce X-rays. However other part of the bunch (center region and the “head”) will get a large horizontal kick and will not produce X-rays because of the large oscillations in the undulator region.

Figure15: A zoomed in out plot from Fig. 2. Wake field kick together with a kick from a horizontal corrector (red line); angle range from -4.5 rad to+4.5 rad (black dashed line) and correspondent time interval ±0.475 fs (green lines). Bunch shape of a bunch “tail”: is shown by a blue line. From this plot we can estimate that R.M.S. of the X-ray pulse length is 0.475 fs for the gap (beam to jaw edge) of 0.15 mm. So in this way we can produce X-ray with R.M.S. duration less that one femtosecond. X-ray pulse length for other gaps will be shown later with experimental results. We can estimate also pulse energy and pulse power of the X-ray pulse. Usually LCLS produce hard Xrays with pulse energy of 2-6 mJ and duration of 30-50 fs. If we use extremum values than we can achieve pulse energy of 300 μJ and pulsed power of 300 GW.

PRIMARY EXPERIMENTAL RESULTS AND INCREASING THE RESOLUTION OF THE TRANSVERSE CAVITY

Figure 14: Pulse energy scan as a function of the magnetic field of the horizontal corrector, which is situated immediately after the horizontal dechirper. To understand what bunch angle in the dechirper region will cancel X-ray production we carried a special energy scan. We measured the energy power of X-rays as a function of the magnetic field of the horizontal corrector,

We carried primary measurement of getting ultra-short Xray pulses. However, we start with the traditional measurement of the X-ray energy loss along the bunch. The Xband deflecting cavity (XTCAV) is used to characterize the FEL x-ray pulse duration and temporal shape. The RF power filling the traverse cavities is coming from 80 MW klystrons with SLED System [24]. The bunch is deflected in the horizontal plane by the high-frequency time variation of the RF field and measured on a downstream (dump) screen after bending in vertical direction with by

the damp magnet. This magnet allows measuring the energy (momentum) spectrum of the beam. So, on the screen we can see energy distribution along the bunch. It happened that when one of the vertical plates of the horizontal dechirper was moved to the beam the image on the dump screen changed [25]. With our proposal for producing the ultra-short X-ray pulses the combine effect of the dechirper and XTCAV can make the resolution of the profile measurement much better. The wake field kick from a corrugated plate near the bunch “tail” region is almost linear (Fig. 2 and Fig. 15). If the phase advance between the horizontal dechirper and the XTCAV is an integer number of 180 degrees then one of the plates of the dechirper will cancel the horizontal kick of the XTCAV and other plate will increase the kick. Fig. 16 shows three images on the dump screen and reconstructed shape of the bunch. The central upper plot shows the image, that is usually used for measuring the energy loss. A part of the image, which has a lilac colour, shows how much energy loss goes for X-ray production. The down central plot shows the reconstructed shape of the bunch. Left plot shows the image when we move the north jaw of the horizontal dechirper to the beam. We can see that the streaking from the XTCAV is strongly decreased. But when we move the south jaw to the beam (right plot) then the streaking is increased more than twice. This is equivalent that we increase the RF power in the XTCAV more than four times, imaging a 360 MW X-band klystron. In addition, the bunch temporal profile resolves much better; we can see that the bunch still has double horns even it was cut from both sides in the first bunch compressor (BC1). Also we can see a short X-ray pulse on the right plot. The scale on the left and right plots is the same as for central plots. Note that we kept the time axis calibrated in femtoseconds as when the dechirper is far from the beam also for the left and right plots. An actual calibration of the non-linear time axis is yet to be performed. In principle we can calibrate the time.

Figure 16: Images of the dump screen and reconstructed bunch temporal profile. The central upper plot shows the image that is usually used of measuring the energy loss. A part of the image, which has a lilac colour, shows how much energy loss goes for X-ray production. The down central plot shows the reconstructed temporal profile of the bunch. Left plot shows the image when we move the north jaw of the horizontal dechirper to the beam. Right plot shows image when we move the south jaw to the

beam. The scale on the left and right plots is the same as for central plots. To make an estimate of the X-ray pulse duration we used a hard X-ray LCLS spectrometer. In SASE regime an image from this spectrometer shows a set of lines of the X-ray spectrum corresponds to the stochastically distributed spikes in the temporal profile of the X-ray pulse. We assume that the number of spikes is large enough that we can use averaged distance between lines in the spectrum. We measure the averaged distance between spectrum lines for different gaps between the beam and the jaw edge of the dechirper and also in the case when a jaw is far away from the beam (no wake field kick). Then we assume that XTCAV gives the right bunch length without wake field kicks and in this way we calibrate the distance between spectrum lines. With this calibration we make an estimate of the X-ray pulse duration. The plots from the spectrometer together with XTCAV dump screen images are shown in Fig. 17. It can be seen that distance between spectrum lines is increasing with decreasing the gap between the beam and the jaw edge.

Figure 17: Images from the LCSL hard X-ray spectrometer for different gaps between the beam and the jaw edge of the horizontal dechirper. Based on this measurement we made comparison of the calculated and measured X-ray pulse duration. The comparison is show in Fig. 18. A blue line shows the calculated pulse duration (previous chapter) and measured R.M.S. pulse length (red diamond). It is surprising that we have more or less good agreement.

Figure 18: Calculated (blue line) and measured (red diamonds) X-ray pulse length.

We also measured the pulse energy of the X-ray pules using LCLS gas detector. The measurement results are shown in Fig. 19 together with estimate values. We may prove that with this method it is possible to produce X-ray pulses shorter that a femtosecond with pulse energy of 0.1 mJ and correspondent power of more than 50 GW. We plan to continue these measurements and determine the stochastic and systematic errors.

Figure 19: Calculated (blue line) and measured (red diamonds) X-ray pulse energy.

SUMMARY The proposed method for the ultra-sort X-ray production at LCLS is very simple and use only two or three operator’s buttons. We may achieve X-ray pules with a duration of less than a femtosecond and with a power of 100 GW or more. Additionally we get twice better (or more) resolution of the measurement of the beam temporal profile using the RF deflecting cavity.

ACKNOWLEDGMENTS The authors would like to thank the LCLS physicists and accelerator operators of the Accelerator Department for their help, especially Benjamin Ripman, Eric Tse and Christopher Zimmer. This work was supported by Department of Energy Contract No. DOE-AC0376SF00515.

REFERENCES [1] www.hamamatsu.com [2] V. Guidi and A. V. Novokhatsky, “A proposal for a radio-frequency-based streak camera with time resolution less than 100 fs”, Meas. Sci. Technol. 6 1555, 1995, doi:10.1088/0957-0233/6/11/001 [3] M. Roehrs, Ch. Gerth, H. Schlarb, B. Schmidt, and P. Schmueser, Phys. Rev. ST Accel. Beams 12, 050704 (2009) [4] Y. Ding et al., “Femtosecond x-ray pulse temporal characterization in free-electron lasers using a transverse deflector”, PR STAB, 14, 120701 (2011)

[5] C. Behrens et al., “Few-femtosecond time-resolved measurements of X-ray free-electron lasers”, Nature Communications vol. 5, 3762 (2014) [6] M. F. Ciappina et al., “Attosecond physics at the nanoscale”,arXiv.org.physics>arHIV:1607.01480 (2016). [7] Zhang Z. et al., “Electron beam energy chirp control with a rectangular corrugated structure at the Linac Coherent Light Source”, Phys. Rev. AB 010702 2015 [8] A. Burov and A. Novokhatski, “A device for bunch selffocusing”, preprint INP 90-82, 1990. [9] A. Novokhatski, “Wakefield potentials of corrugated structures,” Phys. Rev. ST Accel. Beams 18, 104402 (2015). [10] A. Novokhatski, et al., “RadiaBeam/SLAC Dechirper as a Passive Deflector,” in Proceedings, 7th International Particle Accelerator Conference (IPAC 2016): Busan, Korea, May 8-13, 2016, 2016, p. MOPOW046, http://inspirehep.net/record/1469738/files/mopow046 .pdf. [11] A. Novokhatski, “Field dynamics of coherent synchrotron radiation using a direct numerical solution of Maxwell’s equations”, Phys. Rev. ST Accel. Beams, vol. 14, p. 060707, 2011. [12] A. A. Lutman et al, “Fresh-slice multicolour X-ray free-electron lasers”, Nat. Photonics 10, 745 (2016). [13] M. Dal Forno, V. Dolgashev, G. Bowden, C. Clarke, M. Hogan, D. McCormick, A. Novokhatski, B. Spataro, S. Weathersby, and S. G. Tantawi, Phys. Rev. Accel. Beams 19, 011301 (2016). [14] M. Dal Forno, V. Dolgashev, G. Bowden, C. Clarke, M. Hogan, D. McCormick, A. Novokhatski, B. Spataro, S. Weathersby, and S. G. Tantawi, Phys. Rev. Accel. Beams 19, 051302 (2016) [15] M. Dal Forno, V. Dolgashev, G. Bowden, C. Clarke, M. Hogan, D. McCormick, A. Novokhatski, B. O’Shea, B. Spataro, S.Weathersby, and S. G. Tantawi, Phys. Rev. Accel. Beams 19, 111301 (2016). [16] M. D. Forno, V. Dolgashev, G. Bowden, C. Clarke, M. Hogan, D. McCormick, A. Novokhatski, B. O’Shea, B. Spataro, S. Weathersby, and S. G. Tantawi, Nuclear Instruments and Methods in Physics R search Section A: Accelerators, Spectrometers, Detectors and Associated Equipment (2017). http://www.sciencedirect.com/science/article/pii/S01 68900217305557. [17] M. Guetg, et al., “Commissioning of the RadiaBeam/ SLAC Dechirper,” in Proceedings, 7th InternationalParticle Accelerator Conference (IPAC 2016): Busan,Korea, May 8-13, 2016, MOPOW044 http://inspirehep.net/record/1469736/files/mopow044 .pdf. [18] A. Novokhatski, “Calculating the loss factor of the LCLS beamline elements for ultra short bunches”, in Proceedings, of FEL 2009, Liverpool, UK, 2009, WEPC22.

http://accelconf.web.cern.ch/AccelConf/FEL2009/pa pers/wepc22.pdf [19] J. Zemella et al, “Measurement of wake-induced electron beam deflection in a dechirper at the Linac Coherent Light Source,” Phys. Rev. Accel. Beams 20, 104403 (2017). [20] Y.-C. Chao et al., “Control of the Lasing Slice by Transverse Mismatch in an X-Ray Free-Electron Laser”, Phys, Rev. Lett., 121, 064802 (2018) [21] S. Bettoni, P. Craievich, A. A. Lutman and M. Perozi, “Temporal profile measurements of relativistic electron bunch based on wakefield generation,” Phys. Rev. Accel. Beams 19, 021304 (2016) [22] Paolo Craievich and Alberto A. Lutman , “Effects of the quadrupole wakefields in a passive streaker”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Volume 865, 1 September 2017, Pages 55-59. [23] J. Seok et al., “Use of a corrugated beam pipe as a passive deflector for bunch length measurements”, Phys. Rev. AB 21, 022801,2018 [24] J. W. Wang and S. Tantawi, “X-band Travelling Wave RF Deflector Structures”, Proceedings of LINAC08, Victoria, BC, Canada, THP075 http://accelconf.web.cern.ch/accelconf/LINAC08/pap ers/thp075.pdf [25] T. Maxwell, private communication