AbstractThe Inertial electrostatic confinement (IEC) is one of the ways for fusion approaches. It is one of the various methods which can be used to confine hot fusion plasma. The advantage of IEC is that the IEC experiments could be done in smaller size facilities than ITER or NIF, costing less money and moving forward faster. In IEC fusion, we need to trap adequate electrons to confine the desired ion density which is needed for a fusion reactor. Polywell is a device which uses the magnetic cusp system and traps the required amount of electrons for fusion reactions. The purpose of this device is to create a virtual cathode in order to achieve nuclear fusion using inertial electrostatic confinement (Miley and Krupakar Murali, 2014). In this paper, we have simulated the low beta Polywell. Then, we examined the effects of coil spacing, coils current, electron injection energy on confinement time

Mahdavipour, B.

Salar Elahi, A.

Results in Physics

This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/about/our-business/policies/article-withdrawal).This article has been retracted at the request of the Editors-in-Chief.After a thorough investigation, the Editors have concluded that the acceptance of this article was based upon the positive advice of at least two illegitimate reviewer reports. The reports were submitted from email accounts which were provided to the journal as suggested reviewers during the submission of the article. Although purportedly real reviewer accounts, the Editors have concluded that these were not of appropriate, independent reviewers.This manipulation of the peer-review process represents a clear violation of the fundamentals of peer review, our publishing policies, and publishing ethics standards. Apologies are offered to the reviewers whose identities were assumed and to the readers of the journal that this deception was not detected during the submission process.Further, the corresponding author was not able to explain the reason for adding the author name B. Mahdavipour to the revised article

B. Mahdavipour

A. Salar Elahi

Directory of Open Access Journals

RETRACTED: New results on structure of low beta confinement Polywell cusps simulated by comsol multiphysics

Elsevier - Publisher Connector 

Results in Physics 6 (2016) 873–876Contents lists available at ScienceDirect
Results in Physics
journal homepage: www.journals .e lsevier .com/resul ts - in-physicsNew results on structure of low beta confinement Polywell cusps
simulated by comsol multiphysicshttp://dx.doi.org/10.1016/j.rinp.2016.11.003
2211-3797/ 2016 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
⇑ Corresponding author.B. Mahdavipour, A. Salar Elahi ⇑
Plasma Physics Research Center, Science and Research Branch, Islamic Azad University, Tehran, Iran
a r t i c l e i n f o a b s t r a c tArticle history:
Received 15 October 2016
Received in revised form 1 November 2016
Accepted 2 November 2016
Available online 4 November 2016
Keywords:
Low beta confinement
Polywell
IEC
Comsol multiphysicsThe Inertial electrostatic confinement (IEC) is one of the ways for fusion approaches. It is one of the var-
ious methods which can be used to confine hot fusion plasma. The advantage of IEC is that the IEC exper-
iments could be done in smaller size facilities than ITER or NIF, costing less money and moving forward
faster. In IEC fusion, we need to trap adequate electrons to confine the desired ion density which is
needed for a fusion reactor. Polywell is a device which uses the magnetic cusp system and traps the
required amount of electrons for fusion reactions. The purpose of this device is to create a virtual cathode
in order to achieve nuclear fusion using inertial electrostatic confinement (Miley and Krupakar Murali,
2014). In this paper, we have simulated the low beta Polywell. Then, we examined the effects of coil spac-
ing, coils current, electron injection energy on confinement time.
 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Introduction
The Polywell is a nuclear fusion reactor which developed by
Bussard. It is a hybrid device which combines specs and elements
of inertial electrostatic confinement (IEC) and cusped magnetic
confinement fusion [1]. Gridded IEC systems use spherical cathode
grids to create radial electric fields which perform as the deep elec-
trostatic potential wells. The radial electric field causes the ion
confinement and acceleration for fusion reactions in central grid
region [1]. The weakness of these gridded systems is that they lose
lots of energy because of ion collisions with the metal grid. The
Polywell Device uses a system of magnetic cusps to achieve the
necessary electron trapping and create a virtual cathode instead
of the physical cathode. By using a virtual cathode there is no
longer a loss surface embedded within the plasma. The outer grid
which contains the magnetic field coils is effectively isolated by
the magnetic field it creates [2]. Polywell consists of the six current
coil positions of a cube which are three orthogonal pairs of oppos-
ing current loops. The overall system of coils causes magnetic point
cusps centred on the cube faces and corners. Magnetic mirror
effects and reflects electrons towards the magnetic null which
causes Electron confinement [3]. In this paper, we study the con-
finement time for single particle electron as a function of Coil cur-
rent (I), electron energy (K) and the distance of pair coils (coil
spacing) for low beta Polywell device. These calculations have been
done with simulation by Comsol Multiphysics software.Theoretical approach
The magnetic fields were calculated from the Biot-Savart law
with contributions summed over each coil
B ¼ l0I
4p
X
Coils
Z
dl r
r3
ð1Þ
the magnetic fields are time varying, So E, which is calculated from
the magnetic vector potential, A is:
E ¼ dA
dt
ð2Þ
A ¼ l0I
4p
X
Coils
Z
dl r
r
ð3Þ
We assumed that the confinement time scale is small compared to
the rate of change of current in the coils, such that the E and B fields
were approximately constant. From the Lorentz force, the radial
position, R, of an electron within the device is given by [4]
R ¼ R0 þ rg sinðu0 þxcDtÞe^1  ðrg cosðu0 þxcDtÞ 
E
B
DtÞe^2
þ vjjDte^3 ð4Þ
Here, Dt is a small time interval, xc is the cyclotron angular fre-
quency, rg is the gyro-radius, v? and vjj are the velocity components
perpendicular and parallel to the direction of the local magnetic
field, respectively, and R0 and u0 are the initial position and phase,
Fig. 1. (a) Je_Kollasch polywell Model designed and simulated by Comsol Multi-
physics software. (b) From another view.
Fig. 3. Polywell confinement time based on different coil spacing.
874 B. Mahdavipour, A. Salar Elahi / Results in Physics 6 (2016) 873–876respectively, which were both determined by the initial conditions.
The unit vector along the magnetic field direction is given by e^3 and
e^1 is the resultant unit vector perpendicular to e^3. The unit vector,
e^2, is in the direction of e^1  e^3. The co-ordinates used in this deriva-
tion were chosen such that e^1 and e^3 define the direction of the local
x and z axes, respectively. The electron velocity is obtained from
time derivative of Eq. (4):
v ¼ v? cosðu0 þxcDtÞe^1 þ ðv? sinðu0 þxcDtÞ 
E
B
Þe^2 þ vjje^3 ð5Þ
were v? ¼ rgxc [3,4] .Comsol multiphysics
COMSOL Multiphysics is a general-purpose software platform,
based on advanced numerical methods, for modeling, simulatingFig. 2. Particle trajectory simulated by Comsol Multiphysics with difand scientific and engineering problems. COMSOL Multiphysics,
enable to account for coupled or multiphysics phenomena, also
further expanding the simulation platform with dedicated physics
interfaces and tools for electrical, mechanical, fluid flow, and
chemical applications. COMSOL is a flexible platform that allows
users to model all relevant physical aspects of their designs.
Advanced users can go deeper and use their knowledge to develop
customized solutions, COMSOL gives you the confidence to make
the model you want with real-world precision. Certain characteris-
tics of COMSOL become apparent with use. Compatibility standsferent coil spacing (a) 110 cm (b) 120 cm (c) 150 cm (d) 200 cm.
Fig. 4. Shows the parameters of S, r, Bcorner, Bface and Bedge [2,8].
Fig. 6. Polywell confinement time based on different coil current.
B. Mahdavipour, A. Salar Elahi / Results in Physics 6 (2016) 873–876 875out among these. COMSOL requires that every type of simulation
included in the package has the ability to be combined with any
other. This strict requirement actually mirrors what happens in
the real world. Also it is adaptable with other softwares. If you
need of including another physical effect it can be added. If one
of the inputs to your model requires a formula, you can just enter
it. Using tools like parameterized geometry, interactive meshing,
and custom solver sequences, you can quickly adapt to the ebbsFig. 5. Particle trajectory simulated by Comsol Multiphysics withand flows of your requirements. Comsol Multiphysics can be
installed on windows, Linux and Mac OS X [5,6].Simulation and results
In this paper, we simulated the low-density polywell Based on
Je_Kollasch Model [7] by Comsol Multiphysics software. According
to Fig. 1, each coil radius is 50 cm, Coil spacing is 150 cm. Each coildifferent coil current (a) 15 KA (b) 30 KA (c) 45 KA (d) 60 KA.
Fig. 7. Particle trajectory simulated by Comsol Multiphysics with different electron injection energy (a) 10 keV (b) 20 keV (c) 30 keV (d) 40 keV.
Fig. 8. Polywell confinement time based on different electron injection energy.
876 B. Mahdavipour, A. Salar Elahi / Results in Physics 6 (2016) 873–876loop has the 30 KA current. Electron Injection source is a 5 cm
upward shift with 20 keV energy [5]. Also, we study the effect of
coil current, coil spacing and electron injection energy variations
on confinement time.
Figs. 2 and 3 shows that confinement time depends on coil
spacing. 4models were designed with different coil spacing of
110 cm, 120 cm, 150 cm, and 200 cm. The confinement time
decreases by increasing the coil spacing. But in 120 cm spacing,
we have the best confinement (s = 60, r = 50. when ‘‘S” is 1.2 times
‘‘r”, Bface = Bcorner and Bedge is an order of magnitude larger than
both which is the ideal spacing for confinement (Fig. 4) [2,8].4 models were simulated with the different coils current 15 KA,
30 KA, 45 KA, 60 KA. Based on the Figs. 5 and 6, the confinement
time enhancement depends on the coils current increase.
Also, 4 Models of polywells with different electron injection
energy were simulated. The results of confinement time upon to
electron injection with the energy of 10 keV, 20 keV, 30 keV, and
40 keV are shown in Figs. 7 and 8. Based on the figures, the confine-
ment time is decrease by the electron injection energy increasing.
Conclusions
In this paper, we have simulated the low beta Polywell. Then,
we examined the effects of coil spacing, coils current, electron
injection energy on confinement time. Based on results, we can
conclude that particle confinement time strongly depends on coil
spacing, coil current, and electron injection energy. Generally, the
confinement time increases by increasing the coils current,
decreasing the coil spacing and electron injection energy.
References
[1] Miley George H, Krupakar Murali S. Inertial electrostatic confinement (IEC)
fusion. New York: Springer Science+Business Media; 2014.
[2] Carr Matthew, Gummersall David, Cornish Scott, Khachan Joe. Phys. Plasmas
2011;18:112501.
[3] Gummersall David V, Carr Matthew, Cornish Scott, Kachan Joe. Phys Plasmas
2013;20:102701.
[4] Chen F. Introduction to plasma physics and controlled fusion. Plenum press;
1984.
[5] Comsol Multiphysics software users guide (version 4.3); 2012.
[6] Comsol Installation and operation guide (Version 4.3); 2012.
[7] Je Kollasch, Carl Sovinec, John Santarius. Vlasov-Poisson calculations of electron
confinement times in Polywell devices using a steady-state particle-in-cell
method. In: 2014 US-Japan workshop at UW-Madison.
[8] Matthew Carr, Joe Khachan, Conventional point cusp theories applied to the
polywell, The university of Sydney


New results on structure of low beta confinement Polywell cusps simulated by comsol multiphysics 

file:///data/core-remote/dit/data/elsevier/pdf/661/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMjIxMTM3OTcxNjMwMzY5Mg==.pdf

New results on structure of low beta confinement Polywell cusps simulated by comsol multiphysics

Abstract

Similar works

Full text

Available Versions

Directory of Open Access Journals

Elsevier - Publisher Connector