In this case, the electrons return to their

LASER TECHNOLOGY FORACCELERATOR

original energy levels. The resulting quanta or
photons of light have energy equal to thedifference between the energies of the two

1. Introduction

involved levels. Thus, stimulated emission

One of the most significant inventions of theoccurs.

last century is the invention of the laser, which

An atom in an excited state can emit energy

is now used in almost all aspects of sciens anditself, or it can emit when exposed to external

daily life. The word LASER is formed from theradiation, Fig. 1. It is characteristic that theabbreviation of the English phrase "lightquantum that is emitted and the quantum that

amplification

caused the emission are similar to each other.

bystimulated

emissionofradiation".

Thischaracteristic

determines

that

the

Back in 1916, Albert Einstein [1] predictedwavelength of the induced radiation is equal tothe possibility of transition of atoms from athe wave that caused this radiation. In total,

higher energy state to a lower one under

the induced radiation will increase with an

external influence. During this transition, aincrease in the number of electrons that havecertain amount of energy is released, and such

jumped to the upper energy levels.

radiation is called stimulated. Stimulated
radiation is the basis for the operation of lasers.
The principle of laser operation [2, 3] is basedon the stimulated emission of light photons
when exposed to an external electromagnetic
field. As it is known from the high school
physics, the structure of the atom has aplanetary model according to which negatively
charged electrons revolve around a positively
charged nucleus in certain energy orbits. Eachorbit corresponds to a certain value of theelectron energy. In an unexcited state, electrons
are located at low energy levels, which are dueto the minimum energy consumption, can only
absorb the radiation that falls on them. Whenan atom is exposed to radiation, it receives anadditional portion of energy, which provokes
the transition of electrons (one or more) tohigher energy levels of the atom, that is, theelectron goes into an excited state. Energy isabsorbed in strictly defined portions - quanta.
The excited atom strives to return to therelaxed state again, and gives up excess energy,
emitting it in strictly defined portions as well.

Fig. 1 Principle of lasers
In addition, there are inverse systems ofatoms in which electrons are concentrated at
higher energy levels. In such systems, theprocess of quanta emission dominates over theprocess of absorption. Inverse systems are used
to design optical quantum generators (lasers).
The active substance (medium) is placed in an
optical resonator consisting of two parallel
high-quality mirrors, which are placed on bothsides of the active media. The emitted quanta,
getting inside and repeatedly reflecting fromthe mirrors, cross the active media many times,
thereby cause the appearance of similar quantathrough the emission of atoms, where electrons
are in distant orbits. The active medium can be

of different materials, any aggregation state,
and

its

choicedetermined

by

what

characteristics are required from the laser. The
main characteristics of lasers - power andspectral range - depend on the active medium.
Please refer to Fig. 2. The laser effect (lasing)can occur only when the number of atoms in an
excited state exceeds the number of atoms in a
rest state.
A medium with such characteristics can beprepared by pumping it with additional energy

2. The main types of lasers
Gas lasers
The use of gas in a laser as an active medium
has a very important quality - high opticaluniformity, that is, the light beam in the gas is
scattered and distorted to the least extent. The
gas laser is characterized by high directivity
and monochromaticity of radiation, and canalso operate in a continuous mode. The powerof a gas laser can be significantly increased byfrom a certain external source. This operation
called pumping. Pumping can be carried out
under

the

influenceofelectromagnetic

radiation, electric current, electric discharge,
beam of relativistic electrons, as well as
chemical reaction. The kind of energy used
depends on active medium.

Fig. 3 Principle of He-Ne laserusing different methods of excitation and byincreasing the gas pressure. Therefore, theselasers are most often used where a very highdirectivity and monochromaticity of the beamis required. The very first gas laser was createdin 1960 based on a mixture of helium and neon,
which remains the most common to this day,Fig. 3. After that, many different gas lasers
were created, and still in the process ofcreation, where quantum transitions of neutral
ions, atoms and molecules are used in various
ranges of the spectrum of a light beam (fromultraviolet to infrared, and even X-rays). SuchlasersFig. 2 Elements emission bands
Based on everything written above, it ispossible to determine three main parts of thestructure that any laser has in its composition:1) Active media environment2) Power source or pumping system
3) A device for amplifying the emitted light - asystem of mirrors (optical resonator)

arewidelyusedinaccelerator

laboratories as the devices for beamline andaccelerator components alignment.

Semiconductor lasers
Semiconductor lasers operate in the visible
and infrared ranges. They have a number of
uniquecharacteristics

that

make

them

especially valuable in practice. Semiconductor

lasers are characterized by a high, almost 100%

Solid state lasers

efficiency of conversion of electrical energy into

A solid-state laser active medium is activatedcoherent (stimulated) radiation; low degree of

dielectric crystals, glasses, or dielectric crystals

inertia; can work in continuous mode; have awith their own point defects. As activators of

fairly simple design; have the ability to tune

crystals and glasses, ions of rare earth

the

as

elements or ions of the iron group are usuallyavailability of a large number of semiconductor

used. Intrinsic point defects in crystals arisematerials

under the influence of ionizing radiation or byradiationthatwavelength,
can

as

well

continuously

overlap

wavelengths in the range 0.32 - 32 μm, Fig. 4.

additivecoloring.

The

energylevelsof

Unfortunately, semiconductor lasers also haveactivators or intrinsic defects are used to create

their disadvantages - weak directivity ofradiation, which is associated with their small
size;

difficulties

inobtaininghighmonochromaticity of radiation, which is due tothe large width of the spontaneous emission
spectrum. Semiconductor lasers are used when
the coherence and directivity of wave processes
are not particularly important, but small
dimensions and high laser efficiency are

Fig. 5 Principle of Nd:YAG solid-state laser

required. Typically, such lasers are used as aan inverted population. These lasers are widely

pump lasers within large laser systems.

based on a ruby crystal - aluminum oxide(Al2O3), in which about 0.05% of aluminum
atoms are replaced by chromium ions Cr3 +, on
yttrium aluminum garnet (Y3Al5O12), on
glasses doped with neodymium (Nd3 +),terbium (Tb3 +) ions , ytterbium (Yb3 +), etc.
Stimulated radiation of various frequencies is
produced by more than 250 crystals and about
20 glasses.
The

Fig. 4 Principle of semiconductor laser

generation

wavelength

range

of

solid-state lasers extends from the UV to themid-IR region. They operate in pulsed, CW and

Liquid dye lasers
In liquid dye lasers, the active medium is aliquid. An important characteristic of this laser
is the possibility of obtaining high energy andradiation power in pulsed and continuousmodes of operation, using the circulation of theactive liquid for cooling. They are not used inpractice now due to their low emitted energy
and insufficient chemical resistance.

quasi-CW modes and are the main devices fordiagnosing of charged particle beams.
Solid-state lasers are constructed utilizing athree- or four-level scheme. The active elementof these lasers is usually in the form of acircular cylinder or a rectangular bar. The
active element of more complex configurations
is sometimes also used. The most widespread
design contains a cylindrical active element

together with a gas-discharge pump lamp thatand fiber cavity lasers are also called fiberis placed in an illuminator chamber, whichlasers.

concentrates the radiation of the pump lamp

In most cases, the gain medium for fiber

into the active element, Fig. 5. Due to thelasers is fiber doped with rare earth ions such

multiple reflection of the pump radiation fromasthe inner surface of the illuminator chamber,ytterbium

its more complete absorption into the active

praseodymium (Pr3+). One or more laser diodes

element

are used for pumping, Fig.6.

isachieved.

Schemeswithone

erbium(Er3+),(Yb3+),

neodymiumthulium(Nd3+),(Tm3+),

or

pumping lamp for several active elements or
one active element pumping by several or more

Fiber Laser Resonatorlamps is used.

To create a linear cavity of a fiber laser, it is

For existing solid-state lasers, the output

necessary to use some kind of reflector (mirror),

power in the continuous mode can reach 1-3 kWor create a ring cavity (ring fiber laser). Various

with a specific energy output of ~ 10 W per 1

types of mirrors are used in linear resonators of

cm3 of the active medium with an efficiency of ~an optical fiber laser:

3%. The average power of 103 W at a pulse

 In simple laboratory setups, conventional

repetition rate of up to 100 Hz is realized indielectric mirrors can be attached to thepulse-periodic

theperpendicularly cleaved ends of the fiber, as

free-running mode with a pulse duration of 0.1

shown in Fig. 7. This approach, however, is– 1 ms. Solid state lasers occupy a unique place

not very practical for mass production and issolid-statelasersinin the development of lasers. They areeasy-to-maintain devices capable of generatinghigh power energy. For pumping solid-statelasers, LEDs, lamps, and other lasers can beused.

3. Fiber lasers
The term "fiber laser" generally refers to alaser with an optical fiber as gain medium,
although some semiconductor gain medium

Fig. 7 Principle of fiber laser resonatoralso not very reliable.
 Fresnel reflection from the fiber end face isoften sufficient for use as an output mirror ofa fiber laser cavity.
 It is also possible to deposit dielectric
coatings directly on the ends of the fiber,
usually by sputtering. Such coatings can beused for a wide range of reflections.
 Many fiber lasers use fiber Bragg gratings
formed directly in a doped fiber, or in an
undoped fiber soldered to an active layer.

Fig. 6 Principle of fiber laser

The best power characteristics can belasing bandwidth of about 1.5 GHz (wavelength

obtained by using a collimator at the exit ofrange of about 0.002 nm at a center wavelength

light from the fiber and reflecting it back usingof 633 nm), while a titanium-sapphire (Ti:a dielectric mirror (Fig. 7). The intensity at the

Sapphire) solid-state laser has a bandwidth ofmirror is significantly reduced due to the muchabout 128 THz (300 nm wavelength range

larger beam area. However, a small offset cancentered around 800 nm).

lead to significant reflection loss, polarization
dependent loss, etc.
Another option is to use a fiber loop mirror,
based on a fiber sleeve (e.g. 50:50 split ratio)
and a piece of passive fiber, Fig. 8.

Fig. 8 Principle of fiber loop mirror
Most fiber lasers are pumped with one ormore fiber-output diode lasers (laser dioderadiation is injected into the fiber). Light can bepumped directly into the core or into the inner
cladding of the fiber in high-power lasers.

Fig. 10 Principle of laser resonator mode
amplification
The second factor that determines theLaser resonator modes

frequency of laser radiation is the optical

While laser light is perhaps the purest form

resonator of the laser. In the simplest case, itof light, it still depends on more than justconsists of two flat mirrors set opposite to eachfrequency or wavelength. All lasers emit lightother. The active medium of the laser is placed

over some natural bandwidth or frequency

between them (this configuration is called arange. The bandwidth of a laser is determined

Fabry-Perot resonator, Fig. 9). Since light is a

primarily by the active medium included in thewave, when reflected between the mirrors ofdesign of the laser, as well as the frequency

the resonator, the light will interfere with itself

range in which the laser can operate (betterwith amplification and attenuation, whichleads to the formation of standing waves ormodes between the mirrors.
These standing waves form a discrete set of
frequencies known as longitudinal resonatorFig. 9 Fabry-Perot resonatormodes.

Only

these

modes

possesssuchradiation frequencies that are capable ofknown as the bandwidth). For example, aself-sustaining in the cavity of the resonator,

typical helium-neon (He-Ne) gas laser has a

and all other light frequencies are suppressedby destructive interference, Fig. 10. For a

The individual phases of the light waves in

simple flat mirror resonators, the supported

each mode are not fixed and can change

modes are those for which the distance L

randomly due to factors such as thermal

between the mirrors is a multiple of half thevibrations of the laser design. In lasers thatlight wavelength λ: L = qλ / 2, where q is an

supportinteger known as the order of the mode.

interference between modes can cause a

only

a

few

oscillating

modes,

In practice, the distance between the mirrors

beating effect at the laser output, resulting in

L is usually much greater than the wavelength

random intensity fluctuations; in lasers withof light λ, so the corresponding q values aremany thousands of modes, these interference

large (about 105 to 106). Most interesting is theeffects are typically averaged out to a nearfrequency spacing between any two adjacentconstant output intensity, and this is calledmodes q and q +1. This value is specified (for ancontinuous wave operation, Fig. 11.

empty linear resonator of length L) as Δ:, where c is the speed of light (≈ 3 × 108 m/s).
Using the above equations, a small laser with amirror spacing of 30 cm has a longitudinalmode spacing of 0.5 GHz. Thus, for the twolasers discussed above, a helium-neon laser
with a 30 cm resonator and a 1.5 GHz lasing
bandwidth will support up to 3 longitudinalmodes, while a titanium-sapphire laser with abandwidth of 128 THz can support about
250,000

modes.

When

more

than

one

longitudinal mode is excited, the laser is said tooperate in a “multimode mode”. When only one
longitudinal mode is excited, the laser is said tooperate in a “single mode”.
Eachlongitudinalmode hasacertainbandwidth within which this mode is amplified,but usually this bandwidth, determined by the
Q factor of the resonator (see Fabry-Perot
interferometer), is much smaller than the mode
spacing.

If instead of independent oscillations, eachmode

oscillates

with

fixed

relationships

between its phase and the phases of othermodes, the output power of the laser behavesquite differently. Instead of random or constant
outputintensity,intermittently

the

laser

modes

will

interfere

with

each

other,

creating an intensity burst or pulse of light.
Such a laser is called a mode-locked laser or aphase-locked laser. These pulses are separated
in time by τ = 2L / s, where τ is the time during
which the light makes a complete round trip ofthe laser cavity. This time corresponds to thefrequency interval between any two adjacentmodes, Δν = 1 / τ.
Theduration

of

each

light

pulse

is

determined by the number of modes that
oscillate in one phase (in a real laser, it is not

Mode synchronization theory
In a simple laser, each of these modes will
oscillate independently, without a fixed ratio
betweenFig. 11 Principle of mode-locking

themselves

and

other

modes,

essentially like a set of independent lasers
emitting light at slightly different frequencies.

always true that all laser modes will be phaselocked). If N modes are locked with thefrequency interval Δν, then the total width ofthe locked modes is NΔν, and this value is thewider, the shorter the laser pulse duration. In
practice, the actual pulse width is determinedby the shape of each pulse, which in turn iscreate and form a flow of electrons in thedetermined by the exact relationship between

desired [4] form for injection into accelerating

the amplitude and phase of each longitudinal

fields. Although the electron gun usually makes

mode. For example, for a laser generating

up only a small part of the entire system, its

Gaussian pulses, the minimum possible pulse

characteristics have a decisive influence on the

duration Δt is determined by the formula:

final parameters of the electron beam. Electronguns can operate in continuous or pulsed mode.

The value of 0.441 is known as thetime-bandwidth product of the pulse, andvaries with the shape of the pulse. For
ultrashort pulse lasers, the pulse shape is often
the square of hyperbolic secant (sech2), whichcorresponds to a pulse generation interval of
0.315. Using this equation, the minimum pulse
width can be calculated according to themeasured width of the laser spectrum. For ahelium-neon laser with a spectral width of 1.5
GHz, the shortest Gaussian pulse with thisspectral width will have pulse duration of
about 300 ps. For a Ti:Sa laser with abandwidth of 128 THz, this pulse duration is
only 3.4 fs. These values correspond to theshortest possible Gaussian pulses according to
the laser cavity length. In a real mode-locked
laser, the actual pulse width depends on manyother factors, such as the actual pulse shapeand the overall dispersion of the medium.
Also, for generation of a short pulses theAn electron gun is a device that produces abeam of electrons with a given kinetic energy
and a given configuration. The operation of anelectron gun is possible only in a deep vacuum,
so that the electron beam is not scattered whencolliding with molecules of atmospheric gases.
Electron guns used in accelerator technology
can be divided according to the way theygenerate electrons:
1) Electron guns with thermionic emission.
With a long history of development and use,
thermionic cathodes are the most practicalsources for applications that require long lifeand low duty cycle.
2) Electron guns with photoemission.
Photoemission cathodes, Fig. 12 have long
been used in electro-optical devices at low
current densities. The advent of high-intensity
pulsed lasers has prompted the development ofphotocathodesforhigh-energy

andhigh-brightness electron beams. The principle

chirped pulse amplification scheme is in use.
Readers are advised to follow references at thebottom of the article for further learning.

4. Laser application to accelerator
As applied to accelerators, the type andparameters of the laser system are usually
selected based on the needs of the particularapplication.

Generation of charged particles
Electron beams are used in most modern
accelerators as accelerated electron beam
generators. The role of the electron gun is toFig. 13 Photograph of KEK-B photocathodeof operation of the photocathode is as follows:
pulses of high-power laser radiation pullelectrons from the cathode surface from amethod developed under the leadership of Ya.B.

material with a low work function, Fig. 13.

Feinberg [5].

Photoemission

electron

guns

have

some

The laser pulse creates a high intensity of theadvantages over thermionic ones. Among them,accelerating electric field (up to 1014 V / m),there is no heater, which simplifies the design

which makes it possible to reduce the length ofof the gun; higher values of the maximum

the accelerator by several orders of magnitude.
The

beginningof

activeexperimental

development of laser acceleration started in the
mid-1980s by the laser pulses with duration ofless than 1 pc and a power of several hundred
TW. In 2000, the effect of ion acceleration was
discovered [6, 7] when a thin foil was irradiatedwith high-intensity laser pulses. In this case,the laser pulse knocks out a cloud of electrons
from the foil, the electric field of which
accelerates the ions of the gas adsorbed on the
foil surface.
Fig. 12 Schematics of 1.6 cell room temperature,S-band RF gun
current density; higher beam brightness, sinceelectrons have much lower average transverse
momenta. Disadvantages of photocathodes: thepresence of a complex laser system; high

The main disadvantage of laser accelerationis the greater energy and angular spread ofparticlesascomparedtotraditional

accelerators. A possible solution to this problem
in the acceleration of electrons in plasma is
associated with a new acceleration mode,

requirements for the vacuum in the gun;
impossibility of working with high current
densities at low duty cycle due to high average
power of laser radiation.

Laser acceleration
Laser acceleration of charged particles, basedon the use of electric fields created by powerfulpulses of laser radiation in a vacuum or matter.
The use of laser acceleration for electrons was
first proposed by the Japanese physicist K.
Shimoda and the Russian physicists A.A.
Kolomensky and A.N. Lebedev in the early
1960s, immediately after the creation of lasers.
In 1979 the American scientists T. Tajima andFig. 14 Principle of laser plasma acceleration

J.M. Dawson put forward the idea of using

discovered in 2004. This mode uses a laser

lasers to accelerate electrons in plasma. Thispulse whose power is higher than the wakeidea is close to the collective acceleration

wave destruction threshold, and the length iscomparable to the wavelength of plasma

The use of a sharply focused beam of aoscillations. Then a spherical region depleted ofhigh-powerelectrons (the so-called bubble) is formed

divergence allows to develop a monitor for thebehind the pulse, Fig. 14. Plasma electronstransverse

entering this region acquire approximately the(laserwire). Functionally it is similar to asame energy while accelerating. Ion beams of

secondary emission sensor with a moving wire

close energies are supposed to be obtained(wire scanner).

using foil targets, on the surface of which alayer (about 1 nm thick) is created.

laser

with

beam

a

low

size

diffraction

measurements

The main idea of the laserwire monitor is toreplace the metal wire with a thin laser beam.

By the beginning of the 21st century, theThe physical process used is the Compton

following prospects for the practical application

effect, scattering of photons by a particle beam.

of laser acceleration of charged particles are

A detailed theory of the relativistic Compton

being considered:effect is presented, for example, in [10].

 Use of plasma wakefield accelerators for the

Following [11], we write down the main

generation of synchrotron radiation
 Compaction

accelerators

formulas concerning the use of the Compton

forprotonradiography and radiation therapy.

effect for beam diagnostics. If the laser beamcrosses the electron beam at a right angle and Plasma heating in the implementation ofinertial thermonuclear fusion.

the laser power is evenly distributed along thepath of interaction with the beam, the average

A constant developments of laser acceleration

numberofComptongamma

technologies are underway.

described by the expression:quantais,Laser beam profile monitors
A device concept based on the use of Compton

where Ne is the number of particles in the

scattering (laserwire technique) has been

beam; d interaction length;

proposed to measure the transverse beam size

photon density;inLinearis the laser radiation frequency. The Compton

electron-positron colliders with beam energies

scattering cross section σc is related to theof up to several TeV’s and with a highThomson scattering cross section

future linear colliders

luminosity

will

accelerators[8, 9].

apparently
requiring

be

the

first

non-destructive

averageis the power density and ω0by

the ratio:

measurements of micron and submicron beam
sizes in on-line mode. These measurements are

whereis the classical radius of annecessary for continuous adjustment of theelectron;is the relativistic factor, E isbeams phase volume in order to increase thethe energy of the electron beam. The spectrum

luminosity. Typical beam densities in linear
colliderssignificantly

exceedtheof Compton gamma quanta is:valuessufficient for melting and evaporating any
material in a single beam pass, which makes it
impossible

toemission sensors.

use

traditional

secondarywhereis the energy of gamma

quanta, normalized to the energy of electrons.
The maximum photon energy isof such a monitor system can be approximately
The flux of Compton gamma quanta isconcentrated in a cone, the opening angle ofwhich is on the order of the critical angle

doubled by generating a transverse dipole mode
on a half-wave plate mounted in the path of thelaser beam. A high-power laser beam is split
into two directions using a system of mirrors tomeasure both horizontal and vertical beam

By measuring the count rate of scatteredintensity distributions.

gamma quanta (or electrons) as a function of
the position of the laser beam relative to thebeam, it is possible to calculate the transverse
distribution of particles in the beam for known
parameters of the laser beam at the interaction
point. With the help of Compton scattering,using various optical schemes, it is possible tomeasure both the transverse and longitudinal

Fig. 15 Electron and laser beam interaction
geometry

profile of a relativistic electron or positron

The scanning is performed by means of
acousto-optical scanners or mirrors controlledbeam

by piezo drives, Fig. 16. The laser beam isLaser wire monitor

focused before interacting with the electron

In the scheme of transverse beam profile

beam. After the interaction, the electron beamlaserwire monitor, the laser beam is focusedmoves along a curved trajectory in the field of

into a small spot with a Gaussian power

the bending magnet, while Compton gamma

distribution. For a sharply focused laser beamquanta goes in a straight direction and hit thewith a diffractive divergence, the minimum

detector.

attainable rms spot size σr is given by theformula:where λ is the laser wavelength; θ half ofthe laser beam divergence angle in the waist.
The distance at which the laser beam divergesby √2 times the minimum size is called theRayleigh length
the boundaries

and determinesof the usedlaser beamcross-section, Fig.15 . The minimum achievable
light spot size is on the order of the wavelength
λ. A yttrium-aluminum garnet (YAG) or
neodymium-yttrium-lithium-fluoride (Nd: YLF)
laser, operating at higher harmonics, allows
precise scanning of electron beams with atransverse size down to 350 nm. The resolution

Fig. 16 Example of 1um 1.28GeV electron beam
size measurement [12]Assuming that the beam particles and thelaser beam power have a Gaussian transverse
distribution with the rms width σy and σr,
respectively, we can estimate the averagenumber of Compton gamma quanta depending

maxima and minima of the interference

on the displacement along the y axis:

pattern, and the number of Compton gamma
quanta depends weakly on the position of thebeam. If the beam size is much less than thewhere PL is the laser power; σs is the size ofthe interaction area;

The pulsed

power of the laser beam must be on the order ofseveral megawatts in order to obtain several
thousand Compton gamma quanta in one scan
[11].

period of the interference fringes, then thenumber of gamma quanta is proportional to thebrightness of the interference pattern at agiven point. The dependence of the number ofCompton gamma quanta N on the transverse
position of the beam y can be represented as:
where

Laser interferometer
The idea of using the interference patternproduced by two crossed laser beams tomeasure the size of electron beams in thenanometer range was first proposed andsuccessfully tested in the FFTB (Final Focus

is the wave number of laser

radiation. The ratio B / A = 0 if the transverse
size of the beam is much larger than theinteraction region, and B / A = 1 for an
infinitely thin beam. Thus, the beam size canbe calculated from the measured B / A.

Test Beam) experiment at the Stanford Linear
Accelerator Center [13]. The step of theinterference pattern, an example of which isshown in Fig. 17, depends on the laser
wavelength and the angle of intersection of thebeams.

Fig. 18 Schematics of the laser interferencemonitor system
The schematic of the laser interferometer isshown in Fig. 18. The laser beam is divided into
two half, which are directed in the x - y plane

Fig. 17 Principle schematics of the laserinterference monitor and fringe patternfrom different sides to the trajectory of the

The motion of the electron beam across thefringes of the interference pattern leads tomodulation of the intensity of the flux ofComptongamma

quantageneratedbyhigh-energy electrons in the electromagnetic
field of laser radiation. If the beam size is large
compared to the period of the interference
fringes, then the beam always crosses several

electron beam and are focused to one point on
the trajectory. An interference pattern isformed around this point. An electron beam
moving along the z-axis, interacting with thefields of laser beams, produces Compton
gamma quanta, after which it is deflected froma straight path by a bending magnet. The
intensity of the Compton photon flux isrecorded by a detector. A corrector magnet

located in front of the interaction region of theThird, the size of the electron beam changes

beam

along the z axis:

with

the

laser

radiation

providesscanning of the beam across the interference
fringes.
Following [46], let us estimate the intensityof Compton radiation produced by the beamelectrons in the electromagnetic field of laser
beams in the interference region. For anelectron beam with a Gaussian particle density, where σ ∗ y and β ∗ y are the vertical size ofthe beam and the beta function at the center ofthe interaction region. Taking into account all
the above factors, the modulation depth of theCompton gamma-ray flux has the form:

distribution, the modulation of the Compton
gamma-ray flux can be written as follows:

In the FFTB experiment [47] at β * y = 100µm and σz = 50 µm, the correction was 6%. An

where σy is the rms vertical size of theelectron beam; y0 is the vertical position of thecenter of mass of the beam; ky = 2 sinφ/λ.
Integrating above expression we obtain thedependence of the number of Compton gamma
quanta on the beam position:

Nd: YAG laser with a wavelength of 1064 nm (~ω = 1.17 eV) was used. The duration of the laser
pulse is 10 ns, the energy is 100 mJ, the power
density of the laser beam at the focus is ρL =1.3 × 1015 W/m2, and the photon density in one
beam is 2.3 × 1019 cm- 2. The average number of
gamma

quantageneratedbyComptonscattering of electrons by photons of one laser
The modulation depth of the Compton
gamma-ray flux, defined asbeam, is N = 1000 at E = 50 GeV; Ne = 1010.
In the Accelerator test facility at KEK,
similarmonitorisinoperation.

Itdemonstrated a record 1.28 Gev vertical,electron beam size measurements of the level ofis described by the expression:

43.2 nm [14].
.

Thus, we can calculate the beam size σy fromthe measured modulation depth M of theinterference pattern:

5. Conclusion
The given review is not intended to becomplete and cover all the details of presented
apparatus. Readers are advised to follow

In practical consideration, the following

references for deeper understanding of thecorrective factors should be considered. First,

laser

the laser radiation intensity is not uniform inElectro-optic

the transverse profile,measurement [15].

.

Second, the power of the two intersecting laser
beams is not the same, although fortunately
the dependence of the interference patterncontrast on the power imbalance is weak.

physicsandmethods

techniquesforincludingbunchlengthReferences[1] Einstein,

Albert.

Test

"Zum

quantensatz

vonSommerfeld und Epstein." Verh. Deutsch. Phys.
Ges. 19 (1917): 82-92.
[2] Herd, Robert M., Jeffrey S. Dover, and Kenneth
A. Arndt. "Basic laser principles." Dermatologic
clinics 15.3 (1997): 355-372.
[3] Miller, John C., ed. Laser ablation: principles andapplications.

Vol.

28.

Springer

Science&Business Media, 2013.

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