Femtosecond X-rays via Thomson ScatteringOliver Williams

Physics 199U.C.L.A. Department of Physics and Astronomy

Winter 2003

Within many disciplines of science, the theory behind various nanoscale ultra-fast

dynamics has surpassed the abilities of experimental verification. There has been a

growing desire for tools capable of ultra-fast, high resolution imaging in the Angstrom

wavelength range. These femtosecond x-ray sources offer physics, chemistry, biology,

and other applied sciences a new, powerful tool for experimental research.

Light travels the length of a virus in one femtosecond (10 -15 second). Many

chemical and biochemical processes occur in a few picoseconds to less than 100

femtoseconds. The onset of thermal excitation in atoms is approximately 100

femtoseconds [1]. Hence, the necessity of femtosecond sources is obvious.

Ultra-fast sources which probe at x-ray wavelengths offer many advantages. The

Angstrom scale wavelengths of x-rays have the advantage compared to other light

sources (e.g. Ti:S lasers, wavelength ~ 800 nm) in that they give excellent resolution of

incident structures. X-rays are also capable of penetrating atoms and exciting deeper core

electrons, a useful feature in atomic physics. Within biology, current sources are only

capable of imaging surfaces and are unable to probe with wavelengths corresponding to

the “water window” (~22-45 Angstroms) where many biological processes occur and

water absorbs much less radiation. X-rays also offer the advantage in studying crystalline

structures, as the wavelength is approximately that of the lattice structure. The above

aspects of femtosecond x-ray sources have prompted much research, and different

methods of producing this radiation have been suggested.

In this paper, we will focus on sources that are compatible with University-scale

research programs, but larger proposed source facilities will be briefly mentioned. The

allotted budget and space for a source is a consideration as well as the user’s desired

1

source characteristics. To be useful in university research, the source should have the

following aspects:

Low cost and size

Easy tunability to accommodate various users’ experimental parameters

Achievable short wavelength (< 50 Angstroms)

Ultra-fast pulses (few picoseconds to <100 femtoseconds)

High brightness and photon flux/pulse (brightness=1020* is “ideal” [2])

*units for brightness (photons/s mm2 mrad2 0.1% BW)

Much research has gone into the production of femtosecond x-rays by

laser/plasma interactions. These sources can produce high fluxes of x-rays in less than

600 femtosecond pulses. However, this process is not very tunable and as the emitted x-

rays are emitted in a large (4π) solid angle - it is naturally low brightness. Another source

has been proposed to be built at the Brookhaven Accelerator Test Facility (ATF) - a laser

synchrotron source (LSS). These sources would be capable of producing femtosecond

pulses of very high peak and average brightness but requiring a 150 MeV electron beam

and laser pulse energies in the range of 10-20 J [3]. The cost of such facilities could be as

high as several hundred million dollars , putting it clearly out of range for University use.

X-ray free electron lasers (XFEL’s) are also a future possibility and one has been

proposed utilizing the last third of the linac at Stanford Linear Accelerator Center

(SLAC). The XFEL, like the LSS, would be able to produce sub-100 fs pulses with peak

brightness ten orders of magnitude higher than third generation synchrotron sources [4].

The price, unfortunately, is also comparable to LSS’s.

The recent development of small, affordable, high-power (1 TW and 100 mJ) lasers

based on chirped pulse amplification (CPA), capable of producing femtosecond pulses

has produced an interesting insight into tabletop size x-ray source production. The

interaction of this high intensity laser beam (commonly called table-top terawatt lasers, or

T3 lasers) with a relativistic electron beam gives rise to the production of high-energy

photons through a process called Thomson scattering (or Inverse Compton scattering) [5].

Using the laser as an effective undulator with much shorter period than the commonly

2

used magnetic undulators in synchrotron light sources, a much less energetic electron

beam can be used [6], hence reducing the size and cost of the required facility. This

Thomson source also offers a wide tuning range, where source parameters such as photon

energy, brightness, bandwidth, and pulse length can be adjusted directly through the laser

and electron beam parameters as well as the interaction geometry of the beams to obtain

various x-ray characteristics [6]. The Thomson scattering source has the desired high-

brightness, short pulse, “user-friendly” tuning features of a University research tool

capable of measuring on an atomic scale with high spatial and temporal resolution.

The next section is devoted to the theory behind Thomson scattering and includes the

relevant equations for determining source parameters. Using the theory behind Thomson

scattering in the various interaction schemes, an experimental design of the U.C.L.A.

PEGASUS Laboratory electron beam interacting with a terawatt laser pulse produced by

a compact, commercial T3 laser, is then investigated. Further sections discussed are the

necessary modifications to the beam and laser pulse parameters in determining the most

plausible method of obtaining sub-100 fs x-ray pulses. The possible applications using

this source are then discussed and a summary of user source requirements is included.

TheoryThe fundamental workings of radiation production through the interaction of a laser

and relativistic electron beam can be based on the understanding of undulator theory. For

a typical magnetic undulator in a synchrotron light source, as the electrons move down

the undulator, they are deflected transversely by the alternating magnetic field. However,

always associated with an alternating magnetic field in the relativistic electron reference

frame is an alternating electric field (i.e. a propagating electromagnetic field). Using this

analogy, and replacing the magnetic undulator with a laser beam of period 104 times

smaller, the electrons are deflected many more times and contribute to coherent energy

gain using 100 times less energetic electron beams [7] resulting in a wavelength

downshift of the emitted radiation proportional to 1/2. Following Brau [8], we begin

with the resonance condition:

3

,

(1)

where the magnetic undulator period is given by W, the emitted radiation wavelength is

X, and is the electron energy in units of its rest energy. It is obvious then, if the laser

wavelength replaces the magnetic undulator period, a much shorter wavelength of the

emitted radiation can be obtained. This interaction can also be viewed as a collision

between an electron and photon due to light’s wave-particle duality. This treatment of

the system gives rise to the name Thomson scattering. Depending on the reference

frame, it can appear as if the electrons have been energized by the photons upon collision

(Thomson scattering) or, in the reference frame (laboratory frame) where the electrons

are moving relativisticaly, the energy is instead transferred from electrons to photons,

therefore the opposite of Compton scattering (Inverse Compton scattering) [9]. In either

case, the electron beam must be “bent” (accelerated transversely) to produce/observe the

scattered radiation.

The frequency of the scattered photons off the relativistic electron beam is

dependent on the interaction angle ( ) at which the two beams meet (typically ranging

from 90o to 180o, although small-angle Thomson scattering (SATS) has also been a

proposed interaction configuration [10]). Below is a diagram of the interaction

configuration.

4

Figure 1: Diagram of interaction orientations between the electron bunch and laser pulse where We and Le correspond to x and z, respectively, (stated as earlier) is the interaction angle with =180 indicating a head-on collision and x-rays are emitted in a cone of half-angle, . Note that the z-coordinate in the expression for the longitudinal dimension of the electron bunch is also defined to be along the axis of bunch propagation (z-axis).

A frequency upshift of the emitted radiation occurs and is expressed as a function

of the interaction angle, given as [7&11],

,

(2)

where the incident laser frequency is . The maximum observed frequency of

the emitted radiation occurs at =0 with aL2<<1 typically. The energy of the emitted

radiation is therefore just [7],

,

(3)

with h/2 =6.582x10-16 eV-s and Planck’s constant is h and the energy of the emitted

radiation given in keV’s. The wavelength is then simply expressed as [5,7],

,

(4)

where the radiation wavelength is approximately given in Angstroms.

Laser Parameters

A few parameters of the laser beam appear in expressions later in this theory

section and are covered next.

5

As seen in equation (2), the effects of the laser intensity appear in the undulator

strength, aL, and can play a role in the scattered radiation frequency (hence, wavelength).

The peak laser intensity is inverse-square proportional to the laser spot size and can be

written as,

,

(5)

with PL the peak power of the laser beam and w the spot size. The normalized vector

potential of the laser field (wiggler strength) is then expressed in convenient laboratory

units:

.

(6)

A point of interest is the effects of very high laser intensity (I>1016 W/cm2) such

that aL approaches unity and greater. Non-linear effects in the form of generated

harmonics appear which may be used to extend the tuning range of the x-ray source.

However, ponderomotive scattering also starts to occur for aL>1, where the electrons are

deflected from the laser focus point before they are able to scatter the photons therefore

decreasing the total flux of emitted x-rays [10]. Throughout this paper it is assumed

aL2<<1.

The Rayleigh length of the laser beam is given by the general expression,

.

(7)

The Rayleigh length is important as it partly determines the interaction region of

the two beams. A longer Rayleigh range would allow more interaction cycles between

the laser field and the electrons (primarily for backscattering, discussed later) and hence

6

more radiation production. The relevant parameters are the laser spot size W and the

wavelength of the incident laser beam, L.

The observed shape of the laser beam depending on the orientation of the

interaction is also of importance. The RMS Gaussian width of the laser beam is

expressed by [12],

,

(8)

where the rms temporal width is , the spatial laser pulse length is L and c is the speed of

light.

Electron Beam Parameters

Basic properties of the electron beam have also already been shown to influence

the resultant source parameters. The Lorentz correction factor, first appearing in equation

(2), is just the electron beam’s energy given in units of its rest energy and is computed

by,

(9)

where Eb is the energy of the electron beam and m is the mass of an electron. A good

approximation is mc2=0.511 MeV.

There also exists a limitation on the transverse focusing of the electron beam,

which is related to the normalized emittance of the electron bunch, n, the initial beam

size at the last focusing magnet (thin lens approximation used on quadrupole magnet

array), 0, the “focal length” (distance) after this magnet, f (s), and the Lorentz correction

factor, given by,

.

(10)

7

This is derived1 by substituting the expression for the beta-function, into the rms

divergence angle formula, θrms, describing the resultant beam spread following the last

quad due to uncorrelated beam energies, and assuming fs. The focal spot size then

becomes σ(s) by multiplying the angle by s:

.

Configurations

Having established the fundamentals, we turn to the analysis of specific

geometries in Thomson scattering. There are primarily two modes of operation.

Orthogonal Thomson scattering is the configuration where the electron bunch and laser

pulse meet at a 90o angle and the laser pulse essentially “slices out” only a portion of the

electron bunch with which it interacts. The other case is Thomson backscattering where

the two beams collide head-on at 180o. Here, all the electrons in the bunch interact with

the laser pulse but at the cost of an increased radiation pulse length compared to the

orthogonal case. Because both of these interaction schemes are quite different in the

resultant characteristics of the emitted x-rays, they shall be discussed and analyzed

separately.

Orthogonal Thomson Scattering ( =90 o )

In the 90 degree interaction scheme the laser pulse crosses the electron bunch

transversely and so the interaction geometry of the two must be considered more closely.

The effective number of laser periods seen by the electrons is dependent on the

temporal rms Gaussian laser width which can be expressed as [12],

1 Expressions not numbered as no reference is made to them later; they are only for derivation purposes.

8

.

(11)

Each time the electron is deflected (i.e. cycles through one laser period) radiation is

emitted. The number of x-rays per electron emitted from the interaction is [6],

,

(12)

where 1/137 is the fine-structure constant. The strong dependence on aL should be

noted.

The number of scattered x-rays per pulse is related to eqn. (12) but considers the

geometrical orientation of the electrons forming the bunch as well as including other

parameters such as the total number of electrons in the bunch, Ne, the energy of the laser

pulse in Joules, UL, which corresponds to the number of photons in the pulse, and z, the

electron bunch length (note: all ’s below given in m). The total number of x-rays in

each pulse is NX and is expressed in a more useful “lab units” form as [7],

.

(13)

The electron beam energy and normalized emittance are strongly correlated to the

brightness of the x-ray source. The expression for brightness can take the form [6],

,

(14)

9

where the repetition rate of the system, frep, is considered as well as the total beam

divergence, T, and the electron beam rms opening angle, b. The total beam divergence

is composed of three contributing factors: the electron beam rms opening angle, the

intrinsic x-ray beam opening angle (int), and the divergence contribution from the finite

bandwidth (). Equations for these beam aspects [6] are shown below:

(15)

(r=1.2x)

(16)

(17)

.

(18)

The minimum bandwidth, /, is discussed in more detail later in Common

Characteristics.

The x-ray pulse length has a similar form to eqn. (14) as it is determined by the

interaction geometry. The length of the x-ray pulse will be dependent on how long the

laser and electron beam interact. This indicates that tight beam focusing and fast laser

pulses will result in fast x-rays due to a minimized interaction time. The relation between

these parameters and the resultant source pulse length is expressed as [5,7],

10

,

(19)

where X is the temporal pulse length of the scattered x-rays, x and z are the transverse

and longitudinal electron beam sizes and w and L are the transverse and longitudinal

laser beam sizes, respectively.

Thomson Backscattering ( =180 o )

When the electron beam and laser pulse interact in a head-on collision, the

photons scatter backwards off the electrons with increased energy. In this interaction

scheme, the transverse beam sizes of the electron and laser beam must be matched for

optimal electron/photon interaction and hence x-ray production. The effective number of

laser periods seen by an electron is directly proportional to the temporal laser pulse length

and is given by [3],

.

(20)

This leads to an x-ray flux generated by each electron interaction and has the

same form as the orthogonal Thomson scattering case, given by eqn. (13). It is seen in

eqn. (20) then, that increasing the laser pulse length increases the effective number of

laser periods interacting with the electrons, which corresponds to higher x-ray

production.

Because the beams are assumed to be matched transversely (i.e. x=W) and are

counter-propagating, the interaction is much simpler than the 90o case and the number of

x-ray photons produced for each pulse is geometrically only dependent on the Rayleigh

length of the laser. This is the effective longitudinal interaction region where a smaller

Rayleigh length indicates a tighter laser focus (7) (but not smaller than the electron beam

11

focus), and hence denser photon/electron interactions, seen in the expression for the total

flux per pulse [7,12],

,

(21)

which has been conveniently expressed in units of experimental parameters with the laser

energy given in Joules. The brightness of the backscattered photons is then given by an

expression [5] dependent on the transverse and temporal electron bunch sizes, beam

energy, and the number of electrons in the bunch,

,

(22)

where the temporal bunch length is calculated as b=z/c.

This simplified interaction geometry, unlike the orthogonal scattering, makes the

interaction time negligibly dependent on the laser pulse length and the x-ray pulse length

is determined almost entirely by the length of the electron bunch[5,7]:

.

(23)

Having described the special case of 180o scattering, it is worth mentioning

“small-angle” scattering. Small-angle Thomson scattering has been considered as a

viable interaction scheme to produce femtosecond pulses of x-rays due to the laser pulse

slicing the electron bunch from behind as the electron bunch travels. This scheme is

discussed in [10] and the expression for the pulse duration is cited as,

12

.

(24)

The interaction angle here is for a small-angle (i.e. 1). The other required beam

parameters are investigated in [10] and it should be noted that eqn. (24) assumes 1, a

condition which cannot easily be met by most University-controlled electron beam

sources and hence will not be discussed further in this paper.

Common Characteristics

A characteristic common among both interaction configurations is the minimum

bandwidth (25) of the source [3,5]. This has three factors which determine it:

contribution due to the laser periods (26), the intrinsic energy spread of the electron beam

(27), and the emittance broadened spectral width (28). The bandwidth can be expressed

as,

where,

(25)

,

(26)

, and

(27)

13

.

(28)

The peak brilliance of the x-ray source is then just the brightness in a spectral

width [4].

The scattered (”wiggled”) electrons emit radiation as they interact with the laser

beam, but because the electrons are moving so fast, the radiation emitted normal to the

longitudinal (wiggler) axis is Lorentz contracted in the laboratory frame, forming a cone

of radiation in the direction of travel. More energetic electrons therefore cause less

radiation divergence off the longitudinal axis. The entire spectrum of radiation can be

observed within the collection angle of the cone, 2 (i.e. 100% BW [3]), given by the

close approximation [6],

.

(29)

In the next section, a conceptual experimental design of a commercially available

femtosecond terawatt laser interacting with the electron beam produced by the

PEGASUS laboratory at U.C.L.A. shall be discussed as well as the necessary

modifications to the laser and electron beam parameters in both configurations to obtain

sub-100 fs pulses.

The PBPL Femtosecond X-ray FacilityThe PEGASUS (Photoelectron Generated Spontaneous Radiation Source)

Laboratory at U.C.L.A., outfitted with a Ti:S T3 laser, could be used to create the Particle

Beam Physics Laboratory (PBPL) Femtosecond X-ray Facility. A brief discussion of the

electron beam produced in the laboratory follows.

The current Plane Wave Transformer (PWT) Injector utilizes an interchangeable

cathode design, allowing for the use in either thermionic emission or photoinjector mode.

The thermionic emitter is designed to provide cost-effective, high charge (1 nC) bunches.

14

A LaB6 cathode is currently acting as the emitter. The RF power system has been

designed to provide 20 MW of power to the RF photoinjector, a standing wave S-band

electron source [13&14]. The electron beam parameters in photoinjection mode are

shown in Table 1.

The Ti:S T3 laser is an obtainable, affordable, and compact high-power

femtosecond light source. Its parameters are shown in Table 2. The PEGASUS electron

beam interacting with this laser should theoretically be capable of femtosecond x-ray

pulses with relatively high collimation and an experimentally interesting x-ray flux given

beam parameters in Tables 1 and 2. The resultant x-ray characteristics are given in

Tables 3 and 6, while improved parameters are listed in Tables 4, 5, 7, and 8. An

example diagram of an experimental, compact Thomson scattering system is given in

Figure 2, below.

Figure 2: Diagram of example experimental system [15].

The parameters listed in Table 1 assume an electron beam size of 50 m. This is

an acceptable value, which gives an electron beam focusing distance following the last

magnet of (using eq. 10) s=0.3 m assuming the initial transverse beam size of 1 mm.

This should allow enough space after the final focusing magnet for a reasonably sized

interaction region. The reduction of the electron beam size to 25 m (Tables 4 and 7)

results in s=0.15 m, still an acceptable length for an interaction region.

15

Table 1: PEGASUS Electron Beam Parameters

Parameter Value

Energy (Eb) 15 MeV (30)

Energy Spread (E/E) 0.15 %

Normalized Emittance (n) 5 mm-mrad

Charge (electrons/bunch) (Ne) 1 nC (6x109 e-/bunch)

Electron Bunch Length (z/c=b) 5 ps

Beam Size (x) 50 m

Peak Current (Ib) 200 A

Discussion of 90 o Orientation

An electron beam, with the parameters given above, scattering an incident laser

beam (Table 2) in the 90o orientation will depend on a fast laser pulse and tight focusing

to decrease the interaction time and hence produce x-rays on the order of femtoseconds.

This advantage of pulse duration primarily being determined by the transverse beam sizes

and laser pulse length (eqn. 19), is appealing as a reduction in these parameters is

accomplishable by PBPL through stronger focusing, experience which PBPL has in the

design and construction of permanent magnet quadrupoles (PMQ’s) [2].

Table 2: T3 Ti:S Laser Beam Parameters for Thomson scattering

Parameter Value

Wavelength (L) 800 nm

Peak Power (PL) 1 TW

Pulse Energy (UL) 100 mJ

Pulse Duration (W/c=L) 100 (300) fs

Laser Spot Size (W) 50 m

16

A disadvantage and technical obstacle to overcome is that synchronization

between laser and electron pulses is essential to maximize the amount of photon/electron

interactions and therefore obtain maximal output parameters where picosecond timing

jitters are common [1, 2, 13] but <0.5 ps jitters are desired [2]. However, here PBPL is

also experienced in advanced synchronization methods as well as streak-camera imaging

[2] where precision synchronizing electronics are required, thus orthogonal scattering

might be an option for PBPL. Below is a diagram of an example synchronization system.

Figure 3: Diagram of example synchronization system necessary for orthogonal Thomson scattering. Here, as well as in the calculated x-ray parameters, a system repetition rate of 10 Hz is theorized.

The parameters of the emitted x-rays are given in Table 3. Because =90o in eqn.

1, the frequency is shifted by 22 and the resultant x-ray wavelength is 4.4 Angstroms. It

is seen that this orientation is capable of producing 250 fs pulses with a total flux of

5.1x105 photons/pulse emitted into a collection angle of 33 mrad, spanning the entire

spectral width (i.e. /=100%). While this interaction orientation produces very short

pulses of x-rays, the total flux and brightness are rather uninteresting for use as a research

tool (more details are discussed in the Applications section). This can be understood by

the minimal amount of interactions between the two beams due to the transverse

interaction geometry of this orientation (eqn. 13 and 14).

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Table 3: Emitted X-ray Characteristics (90o)Parameter Value

X-ray Energy (EX) 2.8 keV (x=4.4 Angstroms)

Pulse Duration (X) 250 fs

Total Photon Flux (NX) 5.1x105 photons/pulse

Peak Brightness (B) (/=0.1%) 1.5x104*

Collection angle (2) 33 mrad

*units for brightness (photons/s mm2 mrad2 0.1% BW)

Reasonably obtainable modifications to the laser and electron beam parameters

and the resultant changes in the source characteristics are given below.

Table 4: Source characteristics after modifications (90o)

Modifications Brightness Total Flux Pulse Length

Spot size decrease: x , w = 25 m Increased Laser Power: PL=2 TWIncreased Laser Energy: UL=200 mJ

B=1.4x105* Nx=2.0x106 x=150 fs

Obtaining Sub-100 Femtosecond X-ray Pulses

The desire for sub-100 fs pulses is common across many scientific disciplines. To

obtain these ultra-short pulses through orthogonal scattering the beams must be focused

down to reduce the interaction time between the electron and laser beam. Reducing the

spot sizes of the laser and electron beam in the transverse dimensions to 25 m lowers the

x-ray pulse duration to 150 fs from 250 fs (Table 4). If, in addition to reducing the spot

sizes even more to 20 m, the laser pulse is also compressed to 20 fs, we may be able to

obtain x-ray pulses around 100 fs (Table 5).

This tighter focusing and a possible laser energy increase to 200 mJ will

correspondingly increase the total x-ray flux and brightness (equations 13 and 14,

respectively). This produces fluxes on the order of 106 photons per pulse. When only the

parameters required for 100 fs pulses are considered, the resultant flux is 1.3x106

photons/pulse and the brightness is 2.1x104*. This reduced brightness is due to the

18

decreased laser pulse length in eqn. 14. The effects of a reduction of the electron bunch

length are also shown in Table 5, but are considered primarily for the head-on collision.

Table 5: Modifications necessary for sub-100 fs x-ray pulses at (90o)

Modifications Brightness Total Flux Pulse LengthLaser pulse length decrease: L20 fs

Spot size decrease: x , w = 20 mB=2.1x104* NX=1.3x106 X100 fs

Bunch compression: b=100 fs B=7.5x105* NX=9.3x106 X90 fs

Discussion of 180 o Orientation

This scattering configuration has some definite advantages over the orthogonal

interaction. Matching the laser and electron beam sizes transversely and aligning them

in the counter-propagating configuration is of relative ease compared to the necessity of

synchronization in the 90o case. The electron beam parameters are given in Table 1 and

the same laser parameters in Table 2 are used except for an increased laser pulse length of

300 fs to make the effective laser periods encountered by the electrons the same in both

cases. The resultant x-ray characteristics are shown in Table 6. The frequency is up

shifted by 42 due to =180o in eqn. (2). This results in an x-ray wavelength of 2.2

Angstroms. The total x-ray flux is three orders of magnitude higher for backscattering

and is calculated (using eqn. 21) to be 2.4x108 photons/pulse, which is also emitted into a

33 mrad collection angle across the entire x-ray spectrum. The brightness is drastically

higher than for orthogonal scattering and is found to be 4.4x1014* using eqn. (22) for the

given parameters.

Table 6: Emitted X-ray Characteristics (180o)

Parameter Value

X-ray Energy (EX) 5.6 keV (x=2.2 Angstroms)

Pulse Duration (X) 5 ps

19

Total Photon Flux (NX) 2.4x108 photons/pulse

Peak Brightness (B)(/=0.1%) 4.4x1014*

Collection angle (2) 33 mrad

Because the pulse length is primarily determined by the electron bunch length,

much longer laser pulses (picosecond and even nanosecond pulses) may be used to

increase the effective interaction cycles between the electrons and undulator laser field,

therefore increasing the number of photons scattered (x-rays produced) for each electron

(eqn.’s 13&20) [5, 10].

A disadvantage of this interaction is that in order to produce femtosecond x-rays,

femtosecond electron bunches are required (eqn. 23). For our given electron beam

parameters, a bunch length of 5 ps is available, therefore only 5 ps x-ray pulses may be

created. Unfortunately, compressing the electron bunch to sub-100 fs levels is much

more difficult for PBPL to accomplish than tighter focusing and faster laser pulses

(necessary for 90o scattering) as a compressor chicane is not currently available.

Considering the aspects of both configurations, the backscattering orientation promises

the highest brightness and twice as energetic x-rays than the orthogonal scattering as well

as not requiring beam synchronization at the interaction region, making it the most

desirable set-up if electron bunch compression can be achieved. Following is a table

showing the resultant changes in the source characteristics after reasonably obtainable

modifications are made to the laser and electron beam parameters.

Table 7: Source characteristics after modifications (180o)

Modifications Brightness Total Flux Pulse Length

Spot size decrease: x , w = 25 mIncreased Laser Power: PL=2 TWIncreased Laser Energy: UL=200 mJ

B= 5.2x1016* NX= 7.2x109No Change

20

Obtaining Sub-100 Femtosecond X-ray Pulses

As stated earlier, the x-ray pulse length in the 180o orientation is just that of the

electron bunch length. This necessitates the compression of the electron bunch if

femtosecond x-rays are desired. There are various methods through which this may be

achieved. Direct production of a femtosecond electron bunch can be done through a

somewhat “exotic” method by the use of a photocathode gun and plasma-based laser

accelerator techniques. However, a high acceleration gradient is needed in order to

minimize the space-charge effect of the bunch [17], overall not making this a feasible

method.

Bunch selection is another method of creating smaller bunches. This technique

has been used at BNL ATF where the longitudinal dependency of the electron beam on

the transverse position (dispersion) is utilized to select a small bunch out of a larger one

[17]. This obviously reduces the number of electrons per bunch, an undesirable effect

resulting in decreased x-ray flux (eqn. 21).

In addition to the already mentioned magnetic compression where the electron’s

path length dependence on energy is taken advantage of [17], there is also wake field

compression. In this method, it is possible to use the physical imperfections of the

interior of a waveguide to slow down faster electrons in the bunch and in effect compress

it2.

Compressing the electron bunch will have positive effects in both scattering

configurations. Decreasing the electron bunch length from 5 ps to 100 fs increased the

peak brightness for =180o by nearly two orders of magnitude to 2.2x1016*. For =90o,

the result is somewhat less dramatic but still impressive. The brightness and x-ray flux

increased to 7.5x105* and 9.3x106 photons/pulse, respectively (Table 5). As expected for

backscattering, the x-rays are emitted in a 100 fs pulse, but for the orthogonal case, the

pulse is actually reduced to only 90 fs (eqn. 19). The adjustments to the beam parameters

and the corresponding changes in the characteristics of the scattered x-rays are

summarized in Table 8.

2 Undocumented presentation given by Dr. Sven Reiche at UCLA on bunch compression and its application

to femtosecond x-ray production (2003).

21

Table 8: Modifications necessary for sub-100 fs x-ray pulses in 180o scattering

Modifications Brightness Total Flux Pulse Length

Bunch compression: b=100 fs B=2.2x1016* No Change X=100 fs

Below are graphs which show the tuning range of the x-ray wavelength in the

Thomson scattering source by adjusting the interaction angle. The simplicity of

wavelength tuning in this source makes it highly desirable by the user. These plots were

made based on varying in equation (2). Figure 4 shows the range of coarse tuning

(=10o) from 90o to 180o. Figures 5 and 6 show fine tuning around the interaction limits

(90o to 95o and 175o to 180o with =1o).

Interaction angle vs. X-ray wavelength (Coarse tuning 90 to 180 degrees)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

85 95 105 115 125 135 145 155 165 175

Interaction angle (degrees)

X-ra

y w

avel

engt

h (a

ngst

rom

s)

Figure 4: Coarse tuning range of the x-ray wavelength (90o to 180o)

22

Interaction angle vs. X-ray wavelength (Fine tuning 90 to 95 degrees)

4.05

4.1

4.15

4.2

4.25

4.3

4.35

4.4

4.45

89 90 91 92 93 94 95 96

Interaction angle (degrees)

X-ra

y w

avel

engt

h (a

ngst

rom

s)

Figure 5: Fine tuning range of x-ray wavelength near 90o

Interaction angle vs. X-ray wavelength(Fine tuning 175 to 180 degrees)

2.216

2.217

2.218

2.219

2.22

2.221

2.222

2.223

174 175 176 177 178 179 180

Interaction angle (degrees)

X-ra

y w

avel

engt

h (a

ngst

rom

s)

Figure 6: Fine tuning range of x-ray wavelength near 180o

23

ApplicationsThere are many possible applications for this highly collimated, ultra-fast x-ray

source which have a variety of different source requirements. The possibility of x-ray

microscopy arises when considering the applications. Here, there is a five to ten fold

improvement of resolution compared to that of visible light. Its use in structural biology

is based on the x-ray absorption properties of carbon and nitrogen in the “water window”

(wavelength ~ 23.2-43.6 Angstroms) [18]. Within this range, water absorbs radiation less

readily, therefore good contrast with biological samples can be achieved and less energy

must be deposited onto the sample to view it [18]. For the method of holography, the

optimal wavelength extends just outside the upper water window (44 Angstroms) due to

scattering by carbon near its K-edge. The required energy for imaging is high due to

inefficiencies in the imaging optics, yet spatially coherent x-rays are not necessary,

allowing the total flux to be used. In all cases, colloidal gold labeling can be used to

reduce the required source energy. Here, a suspension of gold atoms envelops the sample,

absorbing and scattering the radiation very efficiently [19]. This causes a background

picture of the sample to be formed based on the “shadow” of the gold labeling. As this

radiation is incident on the sample, however, thermal motion will onset and there will be

degradation of the image. This thus requires a fast pulse (<30 ps) for high doses (>2x106

Gy where 1 Gy1 J/kg) of x-rays so that an image can be made before the sample is

destroyed by radiation [19]. Thomson backscattering would be well-suited for this

application with higher brightness than orthogonal scattering and still an acceptable pulse

length.

The ability to create smaller and smaller circuits has created a necessity for

advanced lithography techniques. X-ray lithography offers the higher resolution imaging

necessary to create these tiny circuits. 1 keV x-rays may be used in proximity printing

where the radiation is shined onto a mask and a pattern is transferred to the silicon chip.

High brightness and collimation are desired for this application.

Another form of lithography is deep-etch x-ray lithography. This technique can

be used for micro-machinery (and possibly nano-machinery) where structural heights of

up to 500 microns with lateral dimensions in the micron range with sub-micron precision

can be created. This corresponds to aspect ratios (ratio of height to smallest lateral

24

dimension) of ~100 while for film lithography the ratio3 is only ~2-3 [17]. This allows

for the creation of thicker microstructures and hence more mass and strength. A

proposed nanostructure fabrication facility at LBL’s Center for X-ray Optics would use

just this technique to penetrate deeply into target materials with 5 keV (X3 Angstroms)

x-ray beams to produce highly complex structures and even MEMS (micro-

electromechanical systems) [20]. The beam requirements for deep etch x-ray lithography

are short wavelengths of only 2-3 Angstroms with high flux and collimation [18]. This is

exactly the wavelength range for the 180o interaction, which also produces substantial x-

ray flux. No mention of pulse length requirements were mentioned, therefore it is

assumed that this is not a crucial parameter, hence again Thomson backscattering offers

the most promising source parameters for this application.

Time resolved x-ray absorption fine structure (XAFS) has been proposed for use

in imaging atomic structures during chemical reactions and phase transitions. The

relevant parameters for this technique are photon energies of 1-20 keV (0.62-12.4

Angstroms), and an 80 fs pulse length with a high repetition rate to image the dynamics

of the structure in time [4].

A specific application and proposed experiment at LCLS is the observation of

giant coulomb explosions in atomic clusters (GCEC). Due to the photoionization of the

core electrons of many nuclei (~1012) upon being irradiated, a coulomb ball of charge is

formed. This ball explodes and produces very fast nuclei, resulting in damage to the

irradiated material. The desired source parameters call for a 15 angstrom nominal

wavelength due to the larger inner-shell ionization cross sections, the shortest pulse

possible as higher quality data can be obtained with shorter pulses at 15 Angstroms, and

very high photon flux is necessary to achieve maximum ionization of the sample. As an

example model of source parameters, the x-ray source at LCLS has the following

characteristics [21]:

Photon energy: EX = 850-1000 eV

Total photon flux: NX = 2 x 1013 photons/pulse

Pulse length: X = 233 fs

3 Given ratio is from 1993.

25

The necessary photon energy given here is easily obtainable by PBPL. The total

photon flux in each pulse is somewhat high compared to what PBPL can provide, but no

minimum required flux is mentioned, therefore maybe some useful data can be gathered.

This flux is best obtained by Thomson backscattering, however, the pulse length of 233 fs

produced by the LCLS source is only realistically obtainable through the orthogonal

scattering scheme if bunch compression is not an option. Following is a summary table

of the applications and their associated source parameter requirements.

Table 9: Summary of applications and required source parameters

Application Pulse Length Photon Flux X (Angstroms)

GCEC 233 fs 2 x 1013? 15

Holography <30 ps ? 44

X-ray Lithography ? ? 12

Deep Etch X-ray Litho. ? ? 2-3

X-ray Microscopy <30 ps ? 23.2-43.6

Time resolved XAFS 80 fs ? 0.62-12.4

SummaryThe recent development of table-top terawatt lasers has allowed the production,

within a small facility, of high fluxes of collimated x-rays in ultra-fast pulses. The source

wavelength (photon energy) is dependent on the interaction angle between the electron

and laser beams and other beam parameters can be adjusted to give specific changes to

the source parameters, giving a high degree of tunability. It has been shown that

scattering a laser pulse off a counter-propagating electron beam (backscattering) gives

high fluxes of photons with the pulse length determined by the electron bunch length and

twice as energetic photons than in the 90o orientation. In the 90o case, however, much

faster pulse lengths can be achieved due to being dependent on the transverse interaction

time between the two beams. Total flux in this orientation is significantly (a few orders

of magnitude) lower than in backscattering and the brightness is even lower. An

experimental design using the PEGASUS electron beam at U.C.L.A. and a commercially

26

available table-top terawatt laser has been investigated and the conclusion made that

Thomson backscattering is a promising radiation source.

References[1] http://www-als.lbl.gov/als/science/sci_archive/femto2.html

[2] PBPL Proposal to Stockpile Stewardship (SS) for PLEIADES source

[3] E. Esarey, P. Sprangle, and A. Ting, NIMA, 331, (1993) 545-549.

[4] Conceptual Design of a 500 GeV e+e- Linear Collider with Integrated X-Ray Laser

Facility, Volume II.

[5] I.V. Pogorelski, et al, Physical Review STAB, vol. 3, 090702 (2000).

[6] E. Esarey and W.P. Leemans.

[7] http://accelconf.web.cern.ch/accelconf/pac97/papers/pdf/3V014.PDF

[8] C. A. Brau, Free-Electron Lasers, San Diego, 1990.

[9] http://www.astro.utu.fi/~cflynn/astroII/l7.html

[10] Y. Li, et al, Physical Review STAB, vol. 5, 044701 (2002).

[11] http://accelconf.web.cern.ch/AccelConf/p95/ARTICLES/TPG/TPG07.PDF

[12] K.J. Kim, S. Chattopadhyay, and C.V. Shank, NIMA, 341, (1994) 351-354.

[13] http://pbpl.physics.ucla.edu/pool/pbpl-0600-2002-000056.pdf

[14] S. Telfer, et al, Proceedings of the 2001 Particle Accelerator Conference, Chicago,

2263.

[15] http://atfweb.kek.jp/icfa/2001/box/w2-5_10p.pdf

[16] J. Yang, Proceedings of EPAC 2002, Paris, France,

http://accelconf.web.cern.ch/AccelConf/e02/PAPERS/TUPRI076.pdf

[17] X.J. Wang, Proceedings of the 1999 Particle Accelerator Conference, NY.

[18] LBL-35023, SLAC Report-430, UC-400, December 1-2, 1993.

[19] SLAC Report- 414, October 21, 1992.

[20] LBL Center for X-Ray Optics, January 10, 1992. http://www.lbl.gov/Science-

Articles/Archive/x-ray-lithography.html

[21] LCLS: The First Experiments, September 2002.

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