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Simulation of Bremsstrahlung Production and Emission Process

Syed Bahauddin Alam1,

Md. Nazmus Sakib, Md Sabbir Ahsan, A B M Rafi Sazzad, Imranul Kabir ChowdhuryBangladesh University of Engineering and Technology (BUET), Dhaka

1baha [email protected]

Abstract—Well-nigh of the bremsstrahlung mensurationswith electron cyclotron resonance ion sources have beenexecuted in uninterrupted functioning way conceding infoexclusively on the steady-state bremsstrahlung emanation.Bremsstrahlung irradiation measuring is usually utilized manynosology method acting. At intermediate to elation laser satu-rations preoccupation by the definitive reverse bremsstrahlungsue drop-offs chop-chop and this mechanics alone is deficientto explicate the points of immersion evaluated in recent epochexperiments. The cognitive operation of assimilation of laserfree energy are rudimentary to the study of optical maser-heated atomic plasmas and have received significant care inexperiments. Results and the simulations of bremsstrahlungexpelling by fast electrons using numerical cross sections isdescribed in this paper.

Index Terms—Bremsstrahlung,Emission, photon, MonteCarlo simulation, differential cross sections (DCS).

I. INTRODUCTION

Monte Carlo simulation of electron-photon showers has

become the fundamental tool for the dosimetry of high-

energy electron beams, for the delineation of analytical x-ray

sources, and, in general, for studies of high-energy radiation

transport, used for these studies [1]. By knowing the energy

or velocity dependence many of the characteristic featuresof plasmas can be empathized. Boltzmann distribution is the

general equilibrium velocity distribution function of a colli-

sionless plasma. This Maxwellian plasma entails that it no

longer restrains free energy and, hence, in the plasmas, there

are no energy exchange processes between the particles. It is

then decipherable that the speeds of the subatomic particle

are presumed to be dispersed around the mean velocity [2].

In the head and in the tissue Bremsstrahlung is produced .

The Bremsstrahlung is ignored by most electron beam. For

high energies and for small fields this becomes increasingly

important. With beam radius Bremsstrahlung from the head

prevails and increases [3]. Due to electron-ion Coulomb

collisions that is a binary elastic collision between twocharged particles interacting through their own Electric Field

in plasmas the Bremsstrahlung radiation has received much.

When the ratio of the average distance between particles

is small, charged particles more or less continuously are

dominated by one another’s electrostatic influence, and their

kinetic energies are small compared to the interaction po-

tential energies. Such plasmas are termed strongly coupled.

A typical particle is electrostatically influenced by all of the

other particles within its Debye sphere, but this interaction

very rarely causes any sudden change in its motion. Such

plasmas are termed weakly coupled. In isotropic weakly

coupled plasmas, the electron-ion bremsstrahlung process

is described by the Debye-Hckel potential. Bremsstrahlung

from cerrobend diminutions with changing magnitude ra-

dius because the amount of cerrobend decussate beam

is decreased. These components were distinguished using

measurements in water with variable collimation by 12-cm

thick Lucite or by cerrobend barricades for clinical electron

beams. [4].

The classical Debye-Huckel model depicts the properties

of a low density plasma and represents to a pair correlation

estimation. It has been known that the plasmas depicted

by the Debye-Huckel model are ideal plasmas subsequently

the average fundamental interaction energy between charged

particles is smaller than the intermediate kinetic energy of a

particle [5]. The cognitive operation of assimilation of laser

free energy are rudimentary to the study of optical maser-

heated atomic plasmas and have received significant care in

experiments. Results and the simulations of bremsstrahlung

expelling by fast electrons using numerical cross sections is

described in this paper

I I . SIMULATION OF BREMSSTRAHLUNG PRODUCTION &

EMISSION

Via Radiation Power Mitigation Reaction, the virility of

waste may be weaken. For the sake of weaken the radiotox-

icity of the radioactive material as early as possible,waste

treatment and management is done.

When a laying out electron motions with atomic Elec-

trons, collision energy loss goes on and this consequences

in either ionization or excitation of the nuclei. Large energy

departures pass off less oftentimes where a substantial ratio

of the energy of placing electrons is transported to an orbital

electron, which is named a knock-on collision, and the

expelled electron is pertained to as a δ-ray. This process ismodeled by collision of ’free electron’ as the outermost shell

electrons are loosely colligated. Where the electron loses a

negotiable amount of energy, there takes place “Collisional

Energy Losses”. The rate of energy release by this mechanics

devolves on the electron energy and the ionization free

energy.

While an electron acts with the coulomb field of the

nucleus Bremsstrahlung irradiation is rendered in the con-

tour of photon emanation. Whenever an electron expires

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Fig. 1. Bremsstrahlung production

approximately the nucleus of a particle, it experiences an

electromagnetic drive and egresses in an free energy loss.

The chance of such an interaction derives as the outdo of

the electron’s approximate to the atom belittles. Afterwards

the energy lost is converted to a Bremsstrahlung photon,

this subprogram is referred to as a radiative energy loss.

The uttermost energy of the Bremsstrahlung photon cannot

be more arduous than the resultant electron energy and a

orbit of photon vitalities underneath this assess is developed.

The energy expiration due to outturn of photons per path

distance dz from electrons of energy E =hυmax, where n is

the Bremsstrahlung absolute frequency, is given close to by

the following relationship.

(dE/dZ )rad = 5.343Z 2EN r20

Z −1

3 (1)

where Z is the atomic number, N the number of nuclei

per unit volume and r0 the classical radius of the electron.

The collision stopping power [7] of radioactive element

is as equation

(−dE/dS )coll = ρ(Z/A)z2f (I, β) (2)

where f (I ,β) is a complex function for radioac-

tive resources. The photons developed by excursus of

charged radioactive particle are called ”Bremsstrahlung”.

Bremsstrahlung is released, when the electron is deflected

by both ambient nuclei and ambient electron of unstable

fabric. The radioactive power can be written as equation

(−dE/dS )rad = ρ(N a/A)(E + mec2)Z 2F (E, Z ) (3)

Where is a radioactive function strongly dependent on

radioactive energy. For a relativistic radioactive particle of

rest mass M, with E >> M ec2, it can be shown that the

Fig. 2. Position Vector

radioactive to ionization losses is approximately. From the

equation (3), energy equation can be written as equation,

(−dE/dS )rad(−dE/dS )coll

= 1.4285×10−3EZ (me/M )2 (4)

In equation (3), derivatives of radiational and collisional

energies are negative. In that ratios energy E is divided

up by the amount of 1.4285×10−3 = 700. As Energy

variance is large enough and energy derivatives are negative.

That negative derivatives of energies are multiplied by 700

in equation (8). So, energy reduction of nuclear material

is higher in that case. At that particular energy, as there

is the ratiocination of radiation and collision derivatives,

an electron can move through radioactive waste as it can

lose energy by bremsstrahlung by exciting and ionizing

radioactive wastes. So, Radiation stopping power can lessenthe effect of waste characterization and hence it is primed

for dispensation and conditioning.

Differential cross sections (DCS) [6] which represent the

state of the art in theoretical high-energy Bremsstrahlung

calculations. However, from very rough approximations all

of these codes determine the direction of the photons emitted

in spite of the fact that intrinsic angular distributions “shape

functions” reproducible with the scaled DCS have been free-

floating for a long time. The difficultness is the tremendous

size of the mathematical information needed to define the

DCS as a mapping of the electron energy, the photon energy

and the direction of emission. It has been exacted that

using imprecise shape functions is not a serious problemfor thick targets, because a parallel electron beam is rapidly

randomized by multiple elastic scattering and this ”washes

out” the intrinsic angular distribution, which would then be

relevant only for thin samples.

We conceive the Bremsstrahlung DCS for electrons of

energy E in a rarity, unstructured, single component interme-

diate of atomic number Z. After integration over the angular

apostasy of the missile, the DCS depends only on the energy

W of the photon and the direction of emission, constituted

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Fig. 3. Position Vector for fixed σ

Fig. 4. DCS

by the polar angle u relative to the direction of the projectile,

and can be expressed as

d2σb

dW d(cosΘ)=

dσb

dW

−→P (5)

The shape function obtained from the Kirkpatrick-

Wiedmann-Statham (KWS) fit is

−→P =

σXsin2θ + σY (1 + cos2θ)

(1− βcosθ)2(6)

Using the second-order nonrelativistic perturbation theory,

differential elastic scattering cross section is

dσb

=

1

2Πhυ2 V 2

qdq (7)

dW is the differential probability of emitting a photon

of frequency within dΩ for a given impact parameter when

a projectile electron changes its velocity in collisions with

the target ion. For all impact parameters, dW is given by

the Larmor formula [7] for continuum radiation from an

accelerated electron:

dW =α

4Π2Λ2

| e.q |2dω

ωdΩ (8)

Fig. 5. DCS vs Charge

Fig. 6. DCS vs Potential

The interaction of charged particles cannot be represented

by a pure Coulomb potential but it can be introduced by

effective pair potentials, in the region of partial degenerate

and strong coupling. The corrected Kelbg potential drop

for the electron-positron fundamental interaction in electron-

positron plasmas admitting all quantum effects can be shown

to be [8]

V = −4π2a02 V /(1 + c(γ )) (9)

Here, Electron-positron bremsstrahlung radiation cross

section in electron-positron plasmas in units of πa0 as a

function of the radiation photon energy.

III. CONCLUSION

It can be concluded that the projected algorithmic pro-

gram renders a fast and precise method acting for sample

distribution the free energy and direction of bremsstrahlung

photons. To ensure the reliableness of the algorithmic rule

in general-purpose Monte Carlo models, it is desirable to

have computed shape functions for a denser grid of energies

and atomic numbers and an algorithm for the simulation of

bremsstrahlung emission by fast electrons using numerical

cross sections is described in this paper. The cognitive

operation of assimilation of laser free energy are rudimentary

to the study of optical maser-heated atomic plasmas andhave received significant care in experiments. Results and

the simulations of bremsstrahlung expelling by fast electrons

using numerical cross sections is described in this paper.

ACKNOWLEDGMENTS

The authors would like to thank Mr. Young-Dae Jung for

his papers “Quantum effects on bremsstrahlung spectrum

from electron-positron plasmas” and “Quantum effects on

bremsstrahlung spectrum from electron-positron plasmas”

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published on APPLIED PHYSICS LETTERS for taking the

multitude of conceptions.

REFERENCES

[1] E. Acosta, X. Llovet, F. Salvat; “Monte Carlo simulation of bremsstrahlung emission by electrons” in APPLIED PHYSICS LET-TERS,vol. 80, Issue 17, 2002.

[2] Young-Dae Jung, “Coulomb corrections on the electron-ionbremsstrahlung spectrum from a generalized Lorentzian (kappa)distribution plasma” AIP, vol. 6, Issue 6, 1999.

[3] B. Luther-Davies, “Evidence of resonance absorption in laser-producedplasmas from the polarization and angular dependence of high- energyx-ray bremsstrahlung emission” in American Institute of Physics , pp.209-211, Vol. 32, No.4, 1978

[4] J. A. Bittencourt, “Fundamentals of Plasma Physics Processes” insSpringer , New York, 2004.

[5] D. Zubarev, V. Morozov, and G. Rpke, “Statistical Mechanics of Nonequ- librium Processes” in Basic Concepts, Kinetic TheorysAkademie, Belin , Vol. 1, 1996,

[6] S. M. Seltzer and M. J. Berger, “Nucl. Instrum. Methods Phys.”Res.B 12, 1985.

[7] H. F. Beyer and V. P. Shevelko, “Introduction to the Physics of HighlyCharged Ions” in Institute of Physics, Bristol, 2003.

[8] W. Ebeling, G. Kelbg, and K. Rohde, Ann. Phys. 21,235 (1968).

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