Basic Theory of Inverse Compton (Thomson) Scattering and Conceptual Design of X-ray Source using the PEGASUS Linac at UCLA and a Tabletop Terawatt Laser

Oliver Williams

Physics 199

UCLA 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 (10^-15 sec) x-ray sources offer physics, chemistry, biology, and other applied sciences a new, powerful tool for experimental research.

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.

X-ray free electron lasers (XFEL's) are a future possibility and PBPL at U.C.L.A. is actively involved with the commissioning of LCLS (Linac Coherent Light Source). This project has been proposed utilizing the last third of the linac at Stanford Linear Accelerator Center (SLAC). The XFEL would be able to produce sub-100 fs pulses with peak brightness ten orders of magnitude higher than third generation synchrotron sources [1]. The price, unfortunately, is several hundred million dollars, making it out of University-scale range.

The recent development of small, affordable, high-power (&Mac179;1 TW and &Mac179;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) [2]. Using the laser as an effective undulator with much shorter period than the commonly used magnetic undulators in synchrotron light sources, a much less energetic electron beam can be used [3], 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 [3]. 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 basic 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 UCLA 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.

Theory

The fundamental workings of radiation production through the interaction of a laser and relativistic electron beam can be based classically 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 [4] resulting in a wavelength downshift of the emitted radiation proportional to 1/γ².

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) [5]. 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 90^o to 180^o, although small-angle Thomson scattering (SATS) has also been a proposed interaction configuration [6]). Below is a diagram of the interaction configuration.

Figure 1: Diagram of interaction orientations between the electron bunch and laser pulse where σ_We and σ_Le correspond to σ_x and σ_z, respectively, α (stated as φ earlier) is the interaction angle with α=180 indicating a head-on collision and x-rays are emitted in a cone of half-angle, θ. 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],

, (1)

where the incident laser frequency is. The maximum observed frequency of the emitted radiation occurs at θ=0 with a_L²<<1 typically. The energy of the emitted radiation is therefore just [4],

, (2)

with 'ºh/2''p' =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 [2,4],

, (3)

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.

As seen in equation (1), the effects of the laser intensity appear in the undulator strength of the laser, a_L, 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,

, (4)

with P_L the peak power of the laser beam and σ_w the spot size. The normalized vector potential of the laser field (wiggler strength) is then expressed in convenient laboratory units:

. (5)

A point of interest is the effects of very high laser intensity (I>10¹⁶ W/cm²) such that a_L 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 a_L>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 [6]. Throughout this paper it is assumed a_L²<<1.

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

. (6)

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 more radiation production. The relevant parameters are the laser spot size σ_W and the wavelength of the incident laser beam, λ_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 [8],

, (7)

where the rms temporal width is 's_t, the spatial laser pulse length is σ_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 (1), is just the electron beam's energy given in units of its rest energy and is determined by,

(8)

where E_b is the energy of the electron beam and m is the mass of an electron and the approximation, mc²=0.511 MeV is fairly accurate.

There also exists a limitation on the transverse focusing of the electron beam, which is related to the normalized emittance of the electron bunch, 'e_n, the initial beam size at the last focusing magnet (thin lens approximation used on quadrupole magnet array), σ₀, the "focal length" (distance) after this magnet, f (s), and the Lorentz correction factor, given by,

. (9)

This is derived[1] by substituting the expression for the beta-function, 'b' into the rms divergence angle formula, θ_rms, describing the resultant beam spread following the last quad due to uncorrelated beam energies, and assuming fÈs. 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 90^o 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 180^o. 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 (φ=90°)

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 [8],

. (10)

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 [3],

, (11)

where α=1/137 is the fine-structure constant. The strong dependence on a_L should be noted.

The number of scattered x-rays per pulse is related to eqn. (11) 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, N_e, the energy of the laser pulse in Joules, U_L, which corresponds to the number of photons in the pulse, and σ_z, the electron bunch length (note: all σ's below given in μm). The total number of x-rays in each pulse is N_X and is expressed in a more useful "lab units" form as [4],

. (12)

The x-ray pulse length has a similar form to eqn. (12) 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 [2,4],

, (13)

where τ_X is the temporal pulse length of the scattered x-rays, σ_x and σ_z are the transverse and longitudinal electron beam sizes and σ_w and σ_L are the transverse and longitudinal laser beam sizes, respectively.

Thomson Backscattering (φ=180°)

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 [9],

. (14)

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. (11). It is seen in eqn. (14) 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. σ_x=σ_W) and are counter-propagating, the interaction is much simpler than the 90^o 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 (6) (but not smaller than the electron beam focus), and hence denser photon/electron interactions, seen in the expression for the total flux per pulse [4,8],

, (15)

which has been conveniently expressed in units of experimental parameters with the laser energy given in Joules. 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 [2,4] is determined almost entirely by the length of the electron bunch, where the temporal length is calculated as τ_b=σ_z/c:

. (16)

Having described the special case of 180^o 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 [6] and the expression for the pulse duration is cited as,

. (17)

The interaction angle here is for a small-angle (i.e. φ<<1). The other required beam parameters are investigated in [6] and it should be noted that eqn. (17) assumes γ>>1, a condition which cannot be easily met by most University-controlled electron beam sources and hence will not be discussed further in this paper.

Common Characteristics

The scattered ("wiggled") electrons emit radiation as they interact with the laser beam, but because the electrons are moving near the speed of light, 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, 2θ (i.e. 100% BW [9]), given by the close approximation [3],

. (18)

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 Facility

The 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. 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 [10&11]. 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[2]

The parameters listed in Table 1 assume an electron beam size of 50 μm. This is an acceptable value, which gives an electron beam focusing distance following the last magnet of (using eq. 9) 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 'μm (Tables 4 and 7) results in s=0.15 m, still an acceptable length for an interaction region.

Table 1: PEGASUS Electron Beam Parameters

Parameter	Value
Energy (Eb)	15 MeV (γ=30)
Energy Spread (ΔE/E)	0.15 %
Normalized Emittance (εn)	5 mm-mrad
Charge (electrons/bunch) (Ne)	1 nC (6x109 e-/bunch)
Electron Bunch Length (σz/c=τb)	5 ps
Beam Size (σx)	50 μm
Peak Current (Ib)	200 A

Discussion of 90° Orientation

An electron beam, with the parameters given above, scattering an incident laser beam (Table 2) in the 90^o 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. 13), 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).

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

Parameter	Value
Wavelength (λL)	800 nm
Peak Power (PL)	1 TW
Pulse Energy (UL)	100 mJ
Pulse Duration (σW/c=τL)	100 (300) fs
Laser Spot Size (σW)	50 μm

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 [10,12,13] but <0.5 ps jitters are desired [12]. However, here PBPL is also experienced in advanced synchronization methods as well as streak-camera imaging [12] 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 a system repetition rate of 10 Hz is theorized.

The parameters of the emitted x-rays are given in Table 3. Because φ=90^o in eqn. 1, the frequency is shifted by 2γ² 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. 'Dw'/'w'=100%). While this interaction orientation produces very short pulses of x-rays, the total flux is 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. 12 and 13).

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

Parameter	Value
X-ray Energy (EX)	2.8 keV (λx=4.4 Angstroms)
Pulse Duration (τX)	250 fs
Total Photon Flux (NX)	5.1x105 photons/pulse
Collection angle (2θ)	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 (90^o)

Modifications	Total Flux	Pulse Length
Spot size decrease: σx , σw = 25 μm Increased Laser Power: PL=2 TW Increased Laser Energy: UL=200 mJ	Nx=2.0x106	τx=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 μm 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 μm, 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 (12). 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. 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 (90^o)

Modifications	Total Flux	Pulse Length
Laser pulse length decrease: τLÈ'20 fs Spot size decrease: σx , σw = 20 μm	NX=1.3x106	τXÈ'100 fs
Bunch compression: τb=100 fs	NX=9.3x106	τXÈ'90 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 90^o 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 4γ² due to φ=180^o in eqn. (1). 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. 15) to be 2.4x10⁸ photons/pulse, which is also emitted into a 33 mrad collection angle across the entire x-ray spectrum.

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

Parameter	Value
Pulse Duration (τX)	5 ps
Total Photon Flux (NX)	2.4x108 photons/pulse
Collection angle (2θ)	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) [2, 6].

A disadvantage of this interaction is that in order to produce femtosecond x-rays, femtosecond electron bunches are required (eqn. 16). 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 90^o scattering) as a compressor chicane is not currently available. Considering the aspects of both configurations, the backscattering orientation promises the most x-ray photons 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 (180^o)

Modifications	Total Flux	Pulse Length
Spot size decrease: σx , σw = 25 μm Increased Laser Power: PL=2 TW Increased Laser Energy: UL=200 mJ	NX= 7.2x109	No Change

Obtaining Sub-100 Femtosecond X-ray Pulses

As stated earlier, the x-ray pulse length in the 180^o 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. Bunch selection is a 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 [15]. This obviously reduces the number of electrons per bunch, an undesirable effect resulting in decreased x-ray flux (eqn. 15).

In addition to the magnetic compression technique where the electron's path length dependence on energy is taken advantage of [15], 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 it[3].

Compressing the electron bunch will have positive effects in both scattering configurations. In the backscattering case, only the length of the x-ray pulse is affected. For φ=90^o, the result is decreased pulse length as well as higher total flux, increased to 9.3x10⁶ photons/pulse (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. 13). The adjustments to the beam parameters and the corresponding changes in the characteristics of the scattered x-rays are summarized in Table 8.

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

Modifications	Brightness	Total Flux	Pulse Length
Bunch compression: τb=100 fs	B=2.2x1016*	No Change	τX=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 φ in equation (1). Figure 4 shows the range of coarse tuning ('Df'=10^o) from 90^o to 180^o. Figures 5 and 6 show fine tuning around the interaction limits (90^o to 95^o and 175^o to 180^o with 'Df'=1^o).

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

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

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

Applications

There 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) [15]. 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 [15]. 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 [16]. 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 Gy=1 J/kg) of x-rays so that an image can be made before the sample is destroyed by radiation [16]. Thomson backscattering would be well-suited for this application with higher flux 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 flux 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 dimension) of ~100 while for film lithography the ratio[4] is only ~2-3 [14]. 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 (λ_XÈ'3 Angstroms) x-ray beams to produce highly complex structures and even MEMS (micro-electromechanical systems) [17]. The beam requirements for deep etch x-ray lithography are short wavelengths of only 2-3 Angstroms with high flux and collimation [15]. This is exactly the wavelength range for the 180^o 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 [1].

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 [18]:

á' ''Photon energy: E_X = 850-1000 eV

á' ''Total photon flux: N_X = 2 x 10¹³ photons/pulse

á' ''Pulse length: τ_X = 233 fs

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	lX (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

Summary

The 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 mainly dependent on the electron beam energy and interaction angle between the electron and laser beams. 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 90^o orientation. In the 90^o 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. An experimental design using the PEGASUS electron beam at U.C.L.A. and a commercially available table-top terawatt laser has been investigated and the conclusion made that Thomson backscattering is a promising radiation source.

References

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

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

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

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

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

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

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

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

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

[11] S. Telfer, et al, Proceedings of the 2001 Particle Accelerator Conference, Chicago, 2263.

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

[13] http://www-als.lbl.gov/als/science/sci_archive/femto2.html[OBW1]'

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

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

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

[17] LBL Center for X-Ray Optics, January 10, 1992. http://www.lbl.gov/Science-Articles/Archive/x-ray-lithography.html

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

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Footnotes

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

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

[3] Undocumented presentation given by Dr. Sven Reiche at UCLA on bunch compression and its application to femtosecond x-ray production (Winter 2003).

[4] Given ratio is from 1993.