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the idea of using a corrugated structure as a  dechirper " in a linac - based x - ray fel was first proposed in ref .
the idea was to use a passive device to remove residual energy chirp in the beam before it enters the undulator for lasing .
the original report considered a round structure .
however , to allow for adjustability , it was next proposed to use a corrugated structure in flat geometry .
but because of an unavoidable quadrupole wake excited in flat geometry , the structure is best built in two halves , with one half rotated by 90 degrees with respect to the other , in order to , in principle , have the quad wake forces cancel .
such structures have been built by radiabeam and tested , first at pohang  @xcite and more recently at the linac coherent light souce ( lcls )  @xcite,@xcite .
the radiabeam / lcls dechirper is the first one that has been tested at high energies ( multi gev ) and short bunch lengths ( 10 s of microns ) .    for a nominal set of parameters for the lcls , the dominant wavelength of the wakefields @xmath0  mm  ( see _
@xcite ) . the full bunch length , however , is normally small , @xmath1  @xmath2 m .
thus , we can expect that a model of the longitudinal ( steady - state ) wake that assumes that it is constant and equal to its value at the origin can be used to approximate the wake effects of the beam in such machines .
the real wake will drop from the origin  ( see @xcite ) , and such a model will give a maximum bound of the wake , one that becomes more accurate as the bunch becomes shorter ( assuming it is not so short that the transient component of the wake becomes significant ) .
for the transverse wake , equal to zero at the origin , we use an approximation of a linear function with the constant slope equal to that at the origin .
we will see that , compared to numerically calculating the wakes , we gain by obtaining simple analytical functions that show us the structure of the wakes .
the calculation of wakes of corrugated structures has been performed for round structures , assuming small corrugations and using perturbation methods  @xcite , @xcite . the same has been done for flat geometry  @xcite.time domain simulations have been performed for more accurate results , particularly when the corrugation parameters are not small compared to the dechirper gap  @xcite , @xcite , @xcite .
more recently , a detailed analysis of the radiabeam / lcls dechirper has been performed using field matching methods  @xcite . finally , in ref .
@xcite , for the case of flat geometry and assuming the impedance can be characterized by a surface impedance , equations for the _ generalized _ wakefields , valid for arbitrary bunch length , are derived . by
 generalized " we mean ( point charge ) wake functions for which the transverse positions of driving and test particles are arbitrary , and are not limited to being near the symmetry plane .
we begin the present report with the results of  @xcite and obtain the values at the origin of the ( generalized ) longitudinal wake and the slope of the transverse wakes .
that is enough to obtain an approximation to the energy loss and kick experienced by a pencil beam ( one with no transverse extent ) .
there is some interest in using a dechirper as a fast kicker , by passing a beam close to one jaw ( see _ e.g. _
@xcite , @xcite ) , and the case of the beam near the wall is automatically included .
then , assuming that the transverse beam sizes are small compared to the gap , we derive perturbation solutions of the wakes , valid over a small neighborhood around the beam centroid .
this allows us to find wake effects like slice energy spread increase and projected emittance growth .
next , we briefly investigate the accuracy of our model .
we finally end with conclusions . in the appendix
, we give a more accurate derivation , than found in @xcite , of the flat geometry wakes for arbitrary bunch lengths .
representative beam and machine parameters for the lcls , which will be used in example calculations in this report , are given in table  i. note that the entire radiabeam / lcls dechirper assembly comprises two 2-m - long sections , one oriented horizontally , the other vertically .
the wakes are given here in cgs units ; to convert to mks one merely needs to multiply by @xmath3 , with @xmath4  @xmath5 and @xmath6 is the speed of light .
wakefield induced energy loss , however , has been converted to mks units , for convenience .
.selected beam and machine properties ( at the dechirper ) used in example calculations .
this is a typical combination of parameters found in ref .
the longitudinal bunch distribution is taken to be uniform .
in the current lattice , the first ( second ) dechirper is vertically ( horizontally ) orientated , with positive ( negative ) @xmath7 . [
cols="<,^,^",options="header " , ]     [ table2_tab ]
we began with general expressions for the wakefields in a corrugated structure dechiper with flat geometry , derived in  @xcite .
we took the limits of short bunch length and obtained simplified , approximate expressions for the longitudinal and transverse wakefields , functions that are reasonably accurate for the type of bunch lengths used in _
e.g. _ the lcls .
we then used these functions to obtain , for a short bunch passing through a dechirper : the energy loss as function of gap , the transverse kick as function of beam offset , the slice energy spread , and the emittance growth of the beam .
we performed a thick lens calculation of emittance growth for the two - dechirper system applied to representative lcls bunch and machine parameters and found that the cancellation does indeed work ; the final projected emittance growth is modest : @xmath8 ( 1.12 ) in @xmath9 ( @xmath10 ) .
we briefly investigated the accuracy of our model , and find that it overestimates the wakes by @xmath1130% for the type of parameters considered in this study ( in particular , full bunch length @xmath12  @xmath2 m and dechirper half - gap @xmath13  mm and the bunch on axis ) . for shorter bunches the model becomes more accurate .    in the appendix
we perform a more accurate derivation of the general wake solution for the dechirper ( the starting point of the main work of this report ) than found in ref .
we find that the results of @xcite are valid provided that the bunch length over half gap , @xmath14 , is small , which is indeed the parameter regime of interest .
although in our example calculation the emittance increase was modest , and the cancellation of emittance growth using the two dechirper sections was effective , we would like to point out that large emittance growth is not far away in parameter space , especially if the gap is decreased ( note the @xmath15 dependence in eq .
[ epsf_eq ] ) .
for example , if in the example calculation above we reduce the energy from @xmath16  gev to @xmath17  gev , and the half gap @xmath13  mm to 0.5  mm , we find that @xmath18 . for this example we obtain a large emttance growth for the full , two dechirper , thick lens calculation : @xmath19 ( 2.5 ) in @xmath9 ( @xmath10 ) .
finally , we would like to emphasize that although we started with a surface impedance , the surface impedance itself never is part of the solution .
this means that the results given here are valid not only for the corrugated pipe dechirper , but rather for _ any _ structure with flat geometry where the impedance can be described by a surface impedance .
such problems include the resistive wall , the shallow corrugated structure ( often used as a model for surface roughness ) , and a metallic pipe lined with a thin dielectric layer .
the only condition for their applicability is that the bunch lengths of interest are small compared to the characteristic distance of the problem .
we thank : the team commissioning the radiabeam / lcls dechirper , led by r. iverson , for showing us how the dechirper affects the beam in practice ; j. zemella , who has worked with us and performed numerical calculations of the dechirper wakes ; i. zagorodnov , for making his computer code echo(2d ) available and helping us with its use . work supported by the u.s .
department of energy , office of science , office of basic energy sciences , under contract no .
de - ac02 - 76sf00515 .
we begin from maxwell s equations in which we assume that all quantities depend on time and @xmath20 as @xmath21 with @xmath22 and make the fourier transform over @xmath9 , @xmath23 where @xmath24 denotes a component of the electromagnetic field . to simplify the notation , in what follows
, we drop the hats in the fourier transformed components of the electromagnetic field .
the trajectory of the driving particle has a zero horizontal offset , @xmath25 , but it is offset in the vertical direction , @xmath26 . the current density corresponding to the the driving particle in @xmath27 representation is @xmath28 where @xmath29 is the amplitude of the fourier component of the current .
the electromagnetic field generated by the driving particle satisfy the maxwell equations in free space : @xmath30 the last term on the right - hand side accounts for the current associated with the particle .
given that the solution of these equation is proportional to the current @xmath29 , to simplify notation , below we set @xmath31 ; this makes the last term on the right - hand side of the last equation in   equal to @xmath32 .
the maxwell equations are supplemented by the boundary conditions at the upper and lower walls , @xmath33 where @xmath34 is the surface impedance .
we seek @xmath35 and @xmath36 in the following form @xmath37 where the terms with @xmath38 are due to the presence of the delta function source in   and the amplitudes @xmath39 , @xmath40 , @xmath41 and @xmath42 are arbitrary numbers . substituting these equations into the last equation of   we find the longitudinal electric field
@xmath43 similarly , @xmath44 , @xmath36 and @xmath45 can be expressed through @xmath39 , @xmath40 , @xmath41 and @xmath42 and the hyperbolic functions from the third , fourth and the fifth equations of  .
after that the amplitudes @xmath39 , @xmath40 , @xmath41 and @xmath42 can be found from the four boundary conditions  . substituting them in   we obtain the following result , @xmath46 where @xmath47 and @xmath48 the longitudinal impedance is related to @xmath49 by the following formula @xmath50 where in the last equality we recalled our assumption @xmath51 . substituting   into eq .
gives a general expression for the longitudinal impedance without any assumption .
the expression   that we use in the main body of this paper is obtained from   and   if one takes into account that @xmath52 and also assumes @xmath53 .
the latter is justified for short bunches with @xmath54 . with these assumptions
, we can neglect the last three terms in eq .
, replace @xmath55 , and neglect the term @xmath56 in eq .  .
it is easy to check that with these modifications impedance   is the same as eq .  .
in previous work  @xcite general expressions , valid for arbitrary bunch lengths , were derived for the wakefields of corrugated structures with flat geometry , such as is used in the radiabeam / lcls dechirper . however , the bunch at the end of linac - based x - ray fels  like the lcls  is extremely short , and for short bunches the wakes can be considerably simplified . in this work , 
 we first derive analytical approximations to the short - range wakes . 
 these are generalized wakes , in the sense that their validity is not limited to a small neighborhood of the symmetry axis , but rather extends to arbitrary transverse offsets of driving and test particles . 
 the validity of these short - bunch wakes holds not only for the corrugated structure , but rather for any flat structure whose beam - cavity interaction can be described by a surface impedance . 
 we use these wakes to obtain , for a short bunch passing through a dechirper : estimates of the energy loss as function of gap , the transverse kick as function of beam offset , the slice energy spread increase , and the emittance growth . in the appendix , a more accurate derivation  than is found in  @xcite  of the arbitrary bunch length wakes is performed ; we find full agreement with the earlier results , provided the bunches are short compared to the dechirper gap , which is normally the regime of interest .    keywords : chirp control , relativistic beam , corrugated pipe    slac - pub-16457 + lcls - ii tn-16 - 01 + arxiv submit/1465446 + january 2016