This document analyzes the radial and longitudinal plasma wakefields generated by a Laguerre-Gauss laser pulse through analytical modeling. Key findings include:
1) A Laguerre-Gauss pulse produces a "donut-shaped" wake with larger field amplitudes compared to a Gaussian pulse.
2) The accelerating and focusing regions of a donut wake are better overlapped than a Gaussian wake, improving particle trapping.
3) Positrons can be injected and accelerated in the first half of the donut wake, unlike the Gaussian case.
4) Parameters like laser spot size, amplitude, and pulse duration significantly impact the wakefield properties in ways that could optimize particle acceleration.
Electromagnetic fields of time-dependent magnetic monopoleIOSR Journals
Dirac-Maxwell’s equations, retained for magnetic monopoles, are generalized by introducing
magnetic scale field. It allows the magnetic monopoles to be time-dependent and the potentials to be Lorentz
gauge free. The non-conserved part or the time-dependent part of the magnetic charge density is responsible to
produce the magnetic scalar field which further contributes to the magnetic and electric vector fields. This
contribution makes possible to create an ideal square wave magnetic field from an exponentially rising and
decaying magnetic charge.
Rethinking the dynamics of an accelerated charge from classical concepts. From the idea that radiation
comes from kinetic energy and managing the problem of the auto-energy of a point charge, a system of
non-linear dynamic equations are found and results amenable to experimental verification. In developing, a
relationship between the principle of causality, which affects the direction of time, and the constancy of
mass appears. Another consequence are the fluctuations in the motion of particles, compatible with
Brownian motion and Heisenberg´s indeterminacy principle. The case of gravitational acceleration is also
analyzed, concluding that no electromagnetic radiation is possible and there is no electric field that can
produce a constant acceleration on a point charge. Thus the constant acceleration is an exclusive feature of
gravity.
Rethinking the dynamics of an accelerated charge from classical concepts. From the idea that radiation comes from kinetic energy and managing the problem of the auto-energy of a point charge, a system of non-linear dynamic equations are found and results amenable to experimental verification. In developing, a relationship between the principle of causality, which affects the direction of time, and the constancy of
mass appears. Another consequence are the fluctuations in the motion of particles, compatible with Brownian motion and Heisenberg´s indeterminacy principle. The case of gravitational acceleration is also analyzed, concluding that no electromagnetic radiation is possible and there is no electric field that can produce a constant acceleration on a point charge. Thus the constant acceleration is an exclusive feature of
gravity.
Rethinking the dynamics of an accelerated charge from classical concepts. From the idea that radiation
comes from kinetic energy and managing the problem of the auto-energy of a point charge, a system of
non-linear dynamic equations are found and results amenable to experimental verification. In developing, a
relationship between the principle of causality, which affects the direction of time, and the constancy of
mass appears. Another consequence are the fluctuations in the motion of particles, compatible with
Brownian motion and Heisenberg´s indeterminacy principle. The case of gravitational acceleration is also
analyzed, concluding that no electromagnetic radiation is possible and there is no electric field that can
produce a constant acceleration on a point charge. Thus the constant acceleration is an exclusive feature of
gravity.
Electromagnetic fields of time-dependent magnetic monopoleIOSR Journals
Dirac-Maxwell’s equations, retained for magnetic monopoles, are generalized by introducing
magnetic scale field. It allows the magnetic monopoles to be time-dependent and the potentials to be Lorentz
gauge free. The non-conserved part or the time-dependent part of the magnetic charge density is responsible to
produce the magnetic scalar field which further contributes to the magnetic and electric vector fields. This
contribution makes possible to create an ideal square wave magnetic field from an exponentially rising and
decaying magnetic charge.
Rethinking the dynamics of an accelerated charge from classical concepts. From the idea that radiation
comes from kinetic energy and managing the problem of the auto-energy of a point charge, a system of
non-linear dynamic equations are found and results amenable to experimental verification. In developing, a
relationship between the principle of causality, which affects the direction of time, and the constancy of
mass appears. Another consequence are the fluctuations in the motion of particles, compatible with
Brownian motion and Heisenberg´s indeterminacy principle. The case of gravitational acceleration is also
analyzed, concluding that no electromagnetic radiation is possible and there is no electric field that can
produce a constant acceleration on a point charge. Thus the constant acceleration is an exclusive feature of
gravity.
Rethinking the dynamics of an accelerated charge from classical concepts. From the idea that radiation comes from kinetic energy and managing the problem of the auto-energy of a point charge, a system of non-linear dynamic equations are found and results amenable to experimental verification. In developing, a relationship between the principle of causality, which affects the direction of time, and the constancy of
mass appears. Another consequence are the fluctuations in the motion of particles, compatible with Brownian motion and Heisenberg´s indeterminacy principle. The case of gravitational acceleration is also analyzed, concluding that no electromagnetic radiation is possible and there is no electric field that can produce a constant acceleration on a point charge. Thus the constant acceleration is an exclusive feature of
gravity.
Rethinking the dynamics of an accelerated charge from classical concepts. From the idea that radiation
comes from kinetic energy and managing the problem of the auto-energy of a point charge, a system of
non-linear dynamic equations are found and results amenable to experimental verification. In developing, a
relationship between the principle of causality, which affects the direction of time, and the constancy of
mass appears. Another consequence are the fluctuations in the motion of particles, compatible with
Brownian motion and Heisenberg´s indeterminacy principle. The case of gravitational acceleration is also
analyzed, concluding that no electromagnetic radiation is possible and there is no electric field that can
produce a constant acceleration on a point charge. Thus the constant acceleration is an exclusive feature of
gravity.
Prof Tom Trainor (University of Washington, Seattle, USA)Rene Kotze
TITLE: Two cultures in high energy nuclear physics
Since the mid eighties a community originating within the Bevalac program at the LBNL has sought to achieve formation of a color-deconfined quark-gluon plasma in heavy ion (A-A) collisions using successively higher collision energies at the AGS, SPS, RHIC and now the LHC, emphasizing a flowing dense "partonic" medium as the principal phenomenon. During much of the same period the high energy physics (HEP) community studying elementary collisions (e-e, e-p, p-p) developed the modern theory of QCD, emphasizing dijet production (fragmentation of scattered partons to observable hadrons) as the principal (calculable) phenomenon. Initially it was assumed that the QGP phenomenon in most-central A-A collisions might be distinguished from the HEP dijet phenomenon in elementary collisions. However, strong overlaps in phenomenology have revealed significant conflicts between QGP and HEP "cultures," especially at RHIC and LHC energies. In this talk I review some of the history and contrast an assortment of experimental evidence and interpretations from the two cultures with suggested conflict resolution.
The thesis is about the improvement of the static-light axial current on the lattice and was performed at the University of Wuppertal in 2008, in the framework of the master's course Computer simulation in Science (CSIS)
The meaning of quantum mechanics becomes clearer when we restate Planck's constant and the gravitational constant in natural Planck units. These units reveal hidden structure that improves our understanding of physics and gives new meaning to fundamental ideas.
The Propagation and Power Deposition of Electron Cyclotron Waves in Non-Circu...IJERA Editor
By solving the plasma equilibrium equation, ray equations, and quasi-linear Fokker-Planck equation, the ray
trajectories and power deposition of EC wave has been numerically simulated in non-circular HL-2A tokamak
plasma. The results show that shaping effect and temperature profile has little influence on ECRH, while plasma
density affect propagation and power deposition obviously. when the ordinary mode of EC waves are launched
from the mid-plane and low-field-side, ray trajectories are bended as the parallel refractive index increases and
even recurve to the low-field side when the parallel refractive index reaches to a certain value. Single absorption
decreases with increasing both poloidal and toroidal injection angle, and can be 100% when poloidal injection
angle is 180o and toroidal injection angle is less than 10o.
EFFECT OF ELECTRON-PHONON INTERACTION ON ELECTRON SPIN POLARIZATION IN A QUAN...optljjournal
This paper presents a theoretical model for the effect of electron-phonon interaction, temperature and magnetic field on degree of electron spin polarization in GaAs/InAs quantum dot LED. To describe the dynamics, quantum Langevin equation for photon number and carrier number is used. Simulation results show that degree of electron spin polarization in quantum dot decreases with increase of electron phonon interaction parameter at constant temperature and constant magnetic field which agrees with experimental results in literatures.
Some possible interpretations from data of the CODALEMA experimentAhmed Ammar Rebai PhD
The purpose of the CODALEMA experiment, installed at the Nan\c{c}ay Radio Observatory (France), is to study the radio-detection of ultra-high energy cosmic rays in the energy range of 10^{16}-10^{18} eV. Distributed over an area of 0.25 km^2, the original device uses in coincidence an array of particle detectors and an array of short antennas, with a centralized acquisition. A new analysis of the observable in energy for radio is presented from this system, taking into account the geomagnetic effect. Since 2011, a new array of radio-detectors, consisting of 60 stand-alone and self-triggered stations, is being deployed over an area of 1.5 km^2 around the initial configuration. This new development leads to specific constraints to be discussed in term of recognition of cosmic rays and in term of analysis of wave-front.
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Presentazione di Giulio Gaudiano per l'intervento "Video is King: 10 Strategie per Fare Business con i Video" durante Social Media Strategies 2015, 15 ottobre a Bologna
In poche parole: consigli per usare Google Analytics come efficace strumento SEO.
In tante parole: trovi l'intervento completo con esempi pratici, percorsi da effettuare su Analytics e commenti su
http://top.giorgiotave.it/blog/2011/10/18/google-analytics-seo/
Prof Tom Trainor (University of Washington, Seattle, USA)Rene Kotze
TITLE: Two cultures in high energy nuclear physics
Since the mid eighties a community originating within the Bevalac program at the LBNL has sought to achieve formation of a color-deconfined quark-gluon plasma in heavy ion (A-A) collisions using successively higher collision energies at the AGS, SPS, RHIC and now the LHC, emphasizing a flowing dense "partonic" medium as the principal phenomenon. During much of the same period the high energy physics (HEP) community studying elementary collisions (e-e, e-p, p-p) developed the modern theory of QCD, emphasizing dijet production (fragmentation of scattered partons to observable hadrons) as the principal (calculable) phenomenon. Initially it was assumed that the QGP phenomenon in most-central A-A collisions might be distinguished from the HEP dijet phenomenon in elementary collisions. However, strong overlaps in phenomenology have revealed significant conflicts between QGP and HEP "cultures," especially at RHIC and LHC energies. In this talk I review some of the history and contrast an assortment of experimental evidence and interpretations from the two cultures with suggested conflict resolution.
The thesis is about the improvement of the static-light axial current on the lattice and was performed at the University of Wuppertal in 2008, in the framework of the master's course Computer simulation in Science (CSIS)
The meaning of quantum mechanics becomes clearer when we restate Planck's constant and the gravitational constant in natural Planck units. These units reveal hidden structure that improves our understanding of physics and gives new meaning to fundamental ideas.
The Propagation and Power Deposition of Electron Cyclotron Waves in Non-Circu...IJERA Editor
By solving the plasma equilibrium equation, ray equations, and quasi-linear Fokker-Planck equation, the ray
trajectories and power deposition of EC wave has been numerically simulated in non-circular HL-2A tokamak
plasma. The results show that shaping effect and temperature profile has little influence on ECRH, while plasma
density affect propagation and power deposition obviously. when the ordinary mode of EC waves are launched
from the mid-plane and low-field-side, ray trajectories are bended as the parallel refractive index increases and
even recurve to the low-field side when the parallel refractive index reaches to a certain value. Single absorption
decreases with increasing both poloidal and toroidal injection angle, and can be 100% when poloidal injection
angle is 180o and toroidal injection angle is less than 10o.
EFFECT OF ELECTRON-PHONON INTERACTION ON ELECTRON SPIN POLARIZATION IN A QUAN...optljjournal
This paper presents a theoretical model for the effect of electron-phonon interaction, temperature and magnetic field on degree of electron spin polarization in GaAs/InAs quantum dot LED. To describe the dynamics, quantum Langevin equation for photon number and carrier number is used. Simulation results show that degree of electron spin polarization in quantum dot decreases with increase of electron phonon interaction parameter at constant temperature and constant magnetic field which agrees with experimental results in literatures.
Some possible interpretations from data of the CODALEMA experimentAhmed Ammar Rebai PhD
The purpose of the CODALEMA experiment, installed at the Nan\c{c}ay Radio Observatory (France), is to study the radio-detection of ultra-high energy cosmic rays in the energy range of 10^{16}-10^{18} eV. Distributed over an area of 0.25 km^2, the original device uses in coincidence an array of particle detectors and an array of short antennas, with a centralized acquisition. A new analysis of the observable in energy for radio is presented from this system, taking into account the geomagnetic effect. Since 2011, a new array of radio-detectors, consisting of 60 stand-alone and self-triggered stations, is being deployed over an area of 1.5 km^2 around the initial configuration. This new development leads to specific constraints to be discussed in term of recognition of cosmic rays and in term of analysis of wave-front.
Video is King: 10 Strategie per Fare Business con i VideoGiulio Gaudiano
Presentazione di Giulio Gaudiano per l'intervento "Video is King: 10 Strategie per Fare Business con i Video" durante Social Media Strategies 2015, 15 ottobre a Bologna
In poche parole: consigli per usare Google Analytics come efficace strumento SEO.
In tante parole: trovi l'intervento completo con esempi pratici, percorsi da effettuare su Analytics e commenti su
http://top.giorgiotave.it/blog/2011/10/18/google-analytics-seo/
Slide del workshop Unicom presentate dal Consigliere Nazionale Federico Rossi in occasione del Global Marketing Forum di Lazise svoltasi il 19 Marzo 2013
Influitive's management and leadership lessons for the labMark Organ
Presentation delivered to the research faculty of Sick Kids Hospital in Toronto on best practices in startup management and leadership principles. Highlights include how to create a sense of purpose, alignment, employee engagement, culture, and more.
Presentazione del workshop "Video Branding Strategy - Creare video per promuovere te e la tua startup", tenuto da Giulio Gaudiano (http://www.giuliogaudiano.it) per l'iniziativa #bicgym (http://www.biclazio.it/it/home/parte-il-percorso-bic-gym-di-bic-lazio.bic) dell'incubatore per startup della Regione Lazio (http://www.biclazio.it/). Segui il corso gratis su http://www.guidadigitale.com/
Come la SEO guida le attività di Web Marketing: alberatura dei contenuti,pi...Michele Baldoni
[Case Study] Come la SEO guida le attività di Web Marketing: alberatura dei contenuti,piano editoriale e nuovi canali
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Dr. Dhiraj J. Trivedi presenting Lecture on Carbohydrate metabolism for medical students.
Professor, SDM College of Medical Sciences, Dharwad, Karnataka, India
Artigo que descreve o trabalho feito com o Chandra nos aglomerados de galáxias de Perseus e Virgo sobre a descoberta de uma turbulência cósmica que impede a formação de novas estrelas.
The Effect of RF Power on ion current and sheath current by electrical circui...irjes
Plasma is very important in the development of technology as it is applied in many electronic devices
such as global positioning system (GPS). In addition, fusion and process of plasma requires important elements,
namely, the electron energy distribution. However, plasma glow is a relatively new research field in physics.
There has not been found any previous study on the electric plasma modeling. Thus, this study was aimed to
study plasma modeling especially to find out what was the difference in the number of density and the
temperature of the electron in the plasma glow before and after heated and to discover how was the distribution
of electron and ion in the plasma. This research was conducted at Brawijaya University, Malang, Indonesia in
the Faculty of Science. This exploration began in the middle of June 2013. The data collection and data analysis
were done during a year around until August 2014. In this research, characteristics of plasma were studied to
build model of plasma. It utilized MATLAB dialect program examination framework which result in the
distribution of temperature and current density. The findings show that there has been a large increase in the
number of U, U2 with power, while figures of U1 is stable until middle of curve and then decrease as u but u2
after increase at point then stable. The differences appearing are probably due to the simplifying assumptions
considered in the present model. There was a curve between current in sheath and plasma. And time and sheath
current increased in the beginning then decreased before they experienced another increase.
Polarized blazar X-rays imply particle acceleration in shocksSérgio Sacani
Most of the light from blazars, active galactic nuclei with jets of magnetized plasma that point nearly along the line of sight, is produced by high-energy particles, up to around 1 TeV. Although the jets are known to be ultimately powered by a supermassive black hole, how the particles are accelerated to such high energies has been an unanswered question. The process must be related to the magnetic field, which can be probed by observations of the polarization of light from the jets. Measurements of the radio to optical polarization—the only range available until now—probe extended regions of the jet containing particles that left the acceleration site days to years earlier1–3, and hence do not directly explore the acceleration mechanism, as could X-ray measurements. Here we report the detection of X-ray polarization from the blazar Markarian 501 (Mrk 501). We measure an X-ray linear polarization degree ΠX of around 10%, which is a factor of around 2 higher than the value at optical wavelengths, with a polarization angle parallel to the radio jet. This points to a shock front as the source of particle acceleration and also implies that the plasma becomes increasingly turbulent with distance from the shock.
First experimental realization of a Thermal ratchet using lasers. A thermal ratchet was a device proposed by Feynman that has the apparent ability to extract direct motion from random noise. Translated into Finance, this concept gave birth to the Parrondo paradox, a trading strategy that has the apparent ability to extract profits (positive PL) from random movements in the price of the underlier.
Classical and Quasi-Classical Consideration of Charged Particles in Coulomb F...ijrap
On the basis of the theory of bound charges the calculation of the motion of the charged particle at the Coulomb field formed with the spherical source of bound charges is carried out. Such motion is possible in
the Riemanniam space-time. The comparison with the general relativity theory (GRT) and special relativity theory (SRT) results in the Schwarzshil'd field when the particle falls on the Schwarzshil'd and Coulomb centres is carried out. It is shown that the proton and electron can to create a stable connection with the dimensions of the order of the classic electron radius. The perihelion shift of the electron orbit in the proton field is calculated. This shift is five times greater than in SRT and when corrsponding substitution of the constants it is 5/6 from GRT. By means of the quantization of adiabatic invariants in accordance with the method closed to the Bohr and Sommerfeld one without the Dirac equation the addition to the energy for the fine level splitting is obtained. It is shown that the Caplan's stable orbits in the hydrogen atom coincide with the Born orbits.
CLASSICAL AND QUASI-CLASSICAL CONSIDERATION OF CHARGED PARTICLES IN COULOMB F...ijrap
On the basis of the theory of bound charges the calculation of the motion of the charged particle at the
Coulomb field formed with the spherical source of bound charges is carried out. Such motion is possible in
the Riemanniam space-time. The comparison with the general relativity theory (GRT) and special relativity
theory (SRT) results in the Schwarzshil'd field when the particle falls on the Schwarzshil'd and Coulomb
centres is carried out. It is shown that the proton and electron can to create a stable connection with the
dimensions of the order of the classic electron radius. The perihelion shift of the electron orbit in the
proton field is calculated. This shift is five times greater than in SRT and when corrsponding substitution of
the constants it is 5/6 from GRT. By means of the quantization of adiabatic invariants in accordance with
the method closed to the Bohr and Sommerfeld one without the Dirac equation the addition to the energy
for the fine level splitting is obtained. It is shown that the Caplan's stable orbits in the hydrogen atom
coincide with the Born orbits.
1. Analysis of radial and longitudinal field of plasma wakefield generated by a Laguerre-
Gauss laser pulse
Ali Shekari Firouzjaei and Babak Shokri
Citation: Physics of Plasmas 23, 063102 (2016); doi: 10.1063/1.4953052
View online: http://dx.doi.org/10.1063/1.4953052
View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/23/6?ver=pdfcov
Published by the AIP Publishing
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Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 194.225.24.117 On: Tue, 07 Jun
2016 13:32:01
2. Analysis of radial and longitudinal field of plasma wakefield generated
by a Laguerre-Gauss laser pulse
Ali Shekari Firouzjaei and Babak Shokri
Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839-63113, Iran
(Received 16 February 2016; accepted 17 May 2016; published online 3 June 2016)
In the present paper, we study the wakes known as the donut wake which is generated by Laguerre-
Gauss (LG) laser pulses. Effects of the special spatial profile of a LG pulse on the radial and longi-
tudinal wakefields are presented via an analytical model in a weakly non-linear regime in two
dimensions. Different aspects of the donut-shaped wakefields have been analyzed and compared
with Gaussian-driven wakes. There is also some discussion about the accelerating-focusing phase
of the donut wake. Variations of longitudinal and radial wakes with laser amplitude, pulse length,
and pulse spot size have been presented and discussed. Finally, we present the optimum pulse dura-
tion for such wakes. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4953052]
I. INTRODUCTION
Laser plasma interaction is a central problem in plasma
physics. It is essential to understand its different aspects
which are related to laser plasma acceleration schemes,
advanced fusion concepts, and novel radiation sources.1–8
When a laser pulse propagates through underdense plasma, a
running plasma wave is produced by the ponderomotive
force of the laser pulse. This wave oscillates at the frequency
xp=
ffiffiffi
c
p
, where xp ¼ ð4pn0e2
=mÞ1=2
is the non-relativistic
electron plasma frequency. e, m, and, n0 denote charge,
mass, and density of electrons, respectively, and finally, c is
the electron relativistic factor. The produced accelerating
fields can be three orders of magnitude greater than those in
conventional accelerators.9,10
Many different aspects of
intense laser plasma interactions have been studied at length
in the last decades. In the present work, we concentrate on
the problem of laser wakefield generation when the laser
pulse is not purely Gaussian. In recent years, there has been
an increasing interest on lasers with Laguerre-Gauss (LG)
shape because of their two special properties: special spatial
profile and orbital angular momentum (OAM) states.11–15
The usage of LG laser pulses to control the transverse focus-
ing fields in laser wakefield acceleration was explored,16
and
the influence of higher order Laguerre–Gaussian laser pulses
in electron acceleration was also examined.17
In another
work,18
the angular momentum of particles in the longitudi-
nal direction produced by the LG laser was investigated, and
the enhancement was compared with those produced by the
usual laser pulses.
Recent papers have introduced a new type of wakes
named donut-shaped wake which is produced by LG laser
pulses.19,20
In the present paper, we model the wake gener-
ated by the LG laser pulse in a weakly non-linear regime in
two dimensions. Furthermore, the excited longitudinal and
transverse electrostatic wakefields are obtained via numeri-
cal study of the non-linear formula. We consider several
aspects of the donut-shaped wakes and discuss the advan-
tages and challenges of these types of wakes and finally com-
pare the results with the Gaussian-driven wake case. This
paper has the following structure. In Section II, we drive the
basic equations of our model. In Section III, we present
some conclusions and discuss on the possible implications of
spatial profile effect of laser pulses on longitudinal accelerat-
ing and radial focusing of donut wakes. Finally in Section
IV, the results are summarized.
II. ANALYTICAL INVESTIGATION
To investigate wakefield excitation, we adopt a com-
moving frame ðx ¼ x; y ¼ y; n ¼ z À ct; t ¼ tÞ where (x; y)
are the transverse coordinates and t and z are the time and
propagation distance, repectively.10
We further use the
quasi-static approximation @=@t ! 0.9
When a laser pulse
propagates in low-density plasma in the z direction, a wake-
field will be excited behind the laser pulse, such that the
wakefield satisfies the well-known wave equation9,10
kÀ2
p
@2
/
@2n
¼
1 þ a r; zð Þ2
2 1 þ /ð Þ2
À
1
2
; (1)
where kp ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4pe2n0=mc2
p
is the plasma wave number. This
equation can be solved in two dimensions for the scalar poten-
tial / which is normalized to mc2
=e, and the electric field
which could be inferred through Ezðn; rÞ ¼ ÀE0@/=@n and
Erðn; rÞ ¼ ÀE0@/=@r, where the parameter E0 ¼ mcxp=e
refers to the cold non-relativistic wave breaking limit.9
We use cylindrical coordinates ðr; h; zÞ where r ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffi
x2 þy2
p
is the transverse distance to the axis and h is the azimuthal
angle. The normalized vector potential (aL ¼ eAL
mc2) of the LG
laser pulse is given by aLðn;rÞ¼a0ajjðnÞarðrÞ, where a0 is
the peak laser vector potential; ajjðnÞ is the longitudinal
profile of intensity given by ajjðnÞ¼expðÀðtÀz=cÞ2
=2sl
2
Þ
where sl, the laser pulse duration, is the root-mean-square
(RMS) of length which is related to the full width at half
maximum (FWHM) through sFWHM ¼2
ffiffiffiffiffiffiffiffiffi
2ln2
p
sl; arðrÞ is the
transverse laser profile given by arðrÞ¼cl;pðr=w0Þjlj
expðÀr2
=w0
2
þilhÞLjlj
p ð2r2
=w2
0Þ, where w0 is the laser spot
1070-664X/2016/23(6)/063102/5/$30.00 Published by AIP Publishing.23, 063102-1
PHYSICS OF PLASMAS 23, 063102 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 194.225.24.117 On: Tue, 07 Jun
2016 13:32:01
3. size, Ljlj
p is a Laguerre polynomial with radial index p and az-
imuthal index l, and finally, cl;p are normalizing factors.18,20
As we are interested in the donut type wake, we introduce a
laser pulse with ðl;pÞ¼ð1;0Þ. For convenience, we have
introduced the dimensionless time s¼xpsFWHM. The spatial
coordinates are normalized to 1=kp. Solving the above differ-
ential equation numerically and using the LG laser profile,
we can present and discuss the results for the transverse fo-
cusing and longitudinal accelerating donut wakefield.
III. NUMERICAL RESULTS
In this section, simulation results of the LG laser pro-
duced wake are compared to the results of the Gaussian laser
pulse. Under the baseline simulation conditions, we use a
laser pulse with normalized peak vector potential a0 ¼ 0:3,
normalized FWHM duration sFWHM ¼ kp=2c, where kp is
plasma wavelength, and normalized spot size of w ¼ 20.
Before analyzing the results, it should be noticed that all pa-
rameters are considered the same for both of the mentioned
laser pulses.
First, we compare Gaussian laser produced wakes with
the one generated by a LG laser pulse. Figure 1 shows the
simulated longitudinal accelerating field Ezðn; rÞ and the
transverse focusing field Erðn; rÞ in a weakly nonlinear re-
gime for both types of wake. Longitudinal and transverse
fields of the donut and Gaussian pulse generated wakes are
presented in Figures 1(a), 1(b) and 1(c), 1(d), respectively.
The accelerating phase of positive and negative charged par-
ticles in a donut wake consists of two slices in both sides of
the propagation axis n ¼ 0. The radius of each slice of the
accelerating phase in the donut wake is about a quarter of the
size of the Gaussian-driven wake.
Regarding these figures and considering the same laser
pulse amplitude, spot size, and pulse duration, there will be a
larger wake field for a donut wake (about ten times more).
According to the previous works on Gaussian laser produced
wakes,9
the most interesting and useful situation for charged
particle acceleration is when particles are injected near the
axis. This is different for a donut wake. Particles should be
injected off axis in donut wakes because the longitudinal
accelerating field vanishes or has a minimum on the axis.
According to Figure 1, for the LG case, the radiation source
should be larger than the normal pulse case.
Another important fact which is considered in this paper
is the overlap region for accelerating-focusing phase (AFP).
A particle of charge q propagating in the positive z direction
in the plasma wakefield is accelerated if qEz 0 and is
focused if q@rEr 0. These inequalities define the AFP and
thus determine the volume of space which is useful for elec-
tron trapping and acceleration. Because of the curvature of
the phase surface in the donut wake, the regions of radial fo-
cusing are shifted toward longitudinal accelerating regions,
and consequently, the overlap between the AFP increases
respect to the Gaussian-driven case. In addition, as seen
from Figure 1, the AFP of a donut wake is larger for positive
charged particles than that for the negative ones. The phase
difference between the accelerating and focusing fields is
generally well known in the quasi-linear regime. There exists
a kp=4 region that is both focusing and accelerating for either
electrons or positrons. However, in the quasi-linear case, the
formation of the AFP for positrons is mainly due to the varia-
tion of the transverse shape and intensity of the driver pulse.
It can be seen from Figure 1(b) that the transverse field
phase is shifted backward about p compared to the Gaussian
case. Due to this phase shift, as presented in Figures 1(a) and
FIG. 1. Accelerating and focusing
wakefield generated by, (a) and (b) LG
laser pulse, (c) and (d) Gaussian laser
pulse. Accessible phase regions of fo-
cusing and accelerating for both elec-
trons and positrons are present.
063102-2 A. S. Firouzjaei and B. Shokri Phys. Plasmas 23, 063102 (2016)
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4. 1(b), the AFP for the positive charged particles is situated in
the first half of the bucket, so they could be injected into the
first bucket. This result is in contrast to Figures 1(c) and 1(d)
which show that the first bucket has no AFP for the positive
charges.
This phase shift also leads to a shift in the AFP of the
negative charged particles from the second quarter to the first
quarter in the first bucket. This finding is important in the self
injection process of a highly nonlinear regime and also other
methods of injection in which charged particles are injected
at the rear point of the first plasma wake. In the Gaussian pro-
duced wake, as the background plasma electrons are trapped
in the first half of the wake region (self-injection), negative
charges will experience a radial expulsion force. Therefore,
this will increase the radial emittance, resulting in the produc-
tion of broad energy spectra of charges before being acceler-
ated in the AFP region. In fact, this feature of the donut wake
will be favorable for laser wakefield accelerators (LWFA).
After the above general comparison, we start to investi-
gate parameter sensibility of donut wakes. Plots of Figure 2
show details of variation of the longitudinal and radial fields
versus laser spot size. It is obvious that laser spot size has a
strong effect on both the longitudinal accelerating and radial
focusing field amplitude. Furthermore, the nonlinear effects
of wave steepening and period lengthening are clearly evi-
dent. This will cause an enhancement in nonlinear plasma
wavelength.10
Thus, one can change the wakefield properties
(length and amplitude) by varying the radial profile of the
laser pulse.
To understand more the latest result, Figure 3 is plotted
for varying pulse amplitude and pulse spot size simultane-
ously. It is found out that the longitudinal accelerating field
could be greater than the cold wave breaking limit even for
the quasi-linear laser amplitude case. So, it can be concluded
that there is a transition from the quasi-linear to the non-
linear wake regime. This finding is really important. In previ-
ous works, it was shown that the maximum wake amplitude
for a Gaussian laser pulse in the linear laser amplitude re-
gime is Ez ¼ 0:76a2
0E0, which is really smaller than the cold
wave breaking limit.9,10
In Figure 4, the effect of the pulse duration on the donut
wake is presented while keeping pulse amplitude fixed. At a
fixed electron density, we examine three different pulse
lengths csFWHM ¼ kp=2 ; kp=4 ; kp=6. It is obvious that the
pulse duration influences the wakefields. One could find
FIG. 2. Variation of (a) longitudinal and (b) transverse, component of donut
wakefield with spot size as a function of kpn and kpr for spot size changed to
w ¼ 25.
FIG. 3. Variation of (a) longitudinal (b) transverse donut wakefield as a
function of kpn and kpr. Normalized spot size changed to w ¼ 25 and nor-
malized amplitude changed to a ¼ 0:6 simultaneously.
063102-3 A. S. Firouzjaei and B. Shokri Phys. Plasmas 23, 063102 (2016)
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5. from Figure 4 that the maximum wake amplitude will be
generated by the pulse length csFWHM ¼ kp=2. To find out
the pulse length at which the laser pulse will most efficiently
drives the plasma wave, we plot the maximum normalized
wake amplitude versus the pulse length in Figure 5. It is evi-
dent that the optimum pulse duration for a donut wake occurs
at s ¼ 2:6. This is different from the results reported for the
Gaussian-driven wakes.9,10
IV. SUMMARY AND CONCLUSION
In this paper, we have studied the case of the laser gener-
ated wakefield by an intense LG pulse in a weakly non-linear
regime. An analytical formula was introduced and numerical
results have been demonstrated. We have explained some
general features of the donut wakes and then compared them
with those of the Gaussian produced wakes. This regime
could be well characterized, and the acceleration process
could be optimized for maximum electron and positron ener-
gies. We showed that the donut wake has a larger focusing-
accelerating phase for positive charged particles compared to
the Gaussian wakes. Our results also show that unlike
Gaussian-driven wakes, there is no possibility to inject
charged particles on axis in donut wakes. Finally, variation of
the laser spot size and laser amplitude were presented and
their effects were discussed. In addition, effects of laser pulse
duration were examined, and the optimum pulse duration to
resonantly drive the wakefield was obtained.
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FIG. 4. Longitudinal wakefield gener-
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csFWHM ¼ kp=2, (b) csFWHM ¼ kp=4,
and (c) csFWHM ¼ kp=6.
FIG. 5. Behaviour of normalized maximum donut wake amplitude versus
pulse length.
063102-4 A. S. Firouzjaei and B. Shokri Phys. Plasmas 23, 063102 (2016)
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2016 13:32:01