» In this presentation, preliminary results from a new cylindrical-shaped inertial electrostatic confinement (IEC) fusion device model are going to be reported.

» The model uses a real-time data acquisition from the simulation by solving the Newton’s Equations including the electrical and magnetic forces.

» The many-body approach and finite difference method is used for the particle interactions and particle-chamber interaction.

» The model includes the Coulomb potential and Lorenz force for the particle dynamics.

» In the present talk, the results of the D-D reactions are presented.

» The model considers the fully-ionized media, where an azimuthal homogeneous magnetic field (B) is also applied.

» The simulation data is stored in the MatLab media in order to explore the positions, velocities and energies of the particles.

» Inertial electrostatic confinement (IEC) fusion devices are steady-state machines.

» Having mostly cylindrical and spherical shapes.

» It operates at the order of kV scale fed by a dc or ac source.

» The ions are accelerated into the central region of the chamber by sustaining a negative electrical potential.

» They have a broad application area such as the neutron lithography, steady-state x-ray production, explosive hunt, and fusion energy researches.

» Historically, some milestones are as follows: » 1959 : Elmore, et al studied the equilibrium and stability problem. » 1967 : Hirsch studied the IEC of the ionized fusion gases. » 1973 : Swanson, et al reported the potential well formation in an

inertial electrostatic plasma confinement device. » 1997 : Ohnishi, et al studied the correlation between the potential well

structure and neutron production. » 2000 : Gu et al, performed the experimental study of potential

structure in a spherical device. » 2001 : Ohnishi, et al applied Particle-in-Cell simulation method. » 2003 : Noborio, et al investigated the neutron production rate and its

dependency on pressure by one-dimensional simulations.

» In last 3 years, most of the studies are performed by different groups

in different countries:

Fig. 1. The model of the proposed IEC device with central current rod.

» It has a central current rod, which enables circular magnetic strength

» Primary study includes 300 electrons and ions interacting each other in the chamber.

» The interactions with cathode and walls are made by finite difference method.

» D-D reaction is considered in a fully-ionized media.

Table 1.Physical properties of device*

Cathode radius 0.3 m

Chamber radius 1 m

Chamber height 3 m *These parameters can be easily changed in the code.

» Coulomb interactions:

» Cathode-ion

» Ion-Ion

» Electron-Ion

» Cathode-electron.

Fig. 2. Representation of cathode-ion and ion-ion interactions from top (a) and side (b).

The cathode rods are summed by z heights, which has the charge density λ=Q/h. Thus indice j denotes the rod elements.

(a)

(b)

Cathode-Ion

2 1

3 321 1

  ,N M

i j i imi

i i i x y i y x i x x i z y

j mi j i im

kQ l r kq l ld lE B v B v B v B v B

dt l r l l

k j i

N and M are maximal cathode element and ion/electron number, respectively

For ions:

For electrons:

Cathode-Electron

2 1 1

3 3 321 1 1

   N M M

e j e em e ime

e e ex y e y x ex x ez y

j m me j e em e im

kQ l r kq l l kq l ld lE B v B v B v B v B

dt l r l l l l

k j i

Cathode-Ion Ion-Ion

2 1

3 321 1

  ,N M

i j i imi

i i i x y i y x i x x i z y

j mi j i im

kQ l r kq l ld lE B v B v B v B v B

dt l r l l

k j i

N and M are maximal cathode element and ion/electron number, respectively

For ions:

For electrons:

Cathode-Electron Electron-Electron

2 1 1

3 3 321 1 1

   N M M

e j e em e ime

e e ex y e y x ex x ez y

j m me j e em e im

kQ l r kq l l kq l ld lE B v B v B v B v B

dt l r l l l l

k j i

2 1

3 321 1

  ,N M

i j i imi

i i i x y i y x i x x i z y

j mi j i im

kQ l r kq l ld lE B v B v B v B v B

dt l r l l

k j i

N and M are maximal cathode element and ion/electron number, respectively

For ions:

For electrons: Cathode-Ion Ion-Ion

Cathode-Electron Electron-Electron Electron-Ion

2 1 1

3 3 321 1 1

   N M M

e j e em e ime

e e ex y e y x ex x ez y

j m me j e em e im

kQ l r kq l l kq l ld lE B v B v B v B v B

dt l r l l l l

k j i

Cathode-Ion Ion-Ion Ion-magnetic field

2 1

3 321 1

  ,N M

i j i imi

i i i x y i y x i x x i z y

j mi j i im

kQ l r kq l ld lE B v B v B v B v B

dt l r l l

k j i

N and M are maximal cathode element and ion/electron number, respectively

Cathode-Electron Electron-Electron Electron-Ion Electron-magnetic field

For ions:

For electrons:

2 1 1

3 3 321 1 1

   N M M

e j e em e ime

e e ex y e y x ex x ez y

j m me j e em e im

kQ l r kq l l kq l ld lE B v B v B v B v B

dt l r l l l l

k j i

2 2 2

2

0 0

0 0 0 06 6 6 6

e i e i e i c e i ac cc

a

r r rr rV r V r V

r r

1 2

3 4

5 6

( , )    (1,0),     ( , )   0.5 (1, 3)

,   0.5 1, 3 ,   ,   1,0

,  0.5 1, 3 ,  ,   0.5 1, 3

a a

a a

a a

r x y r r x y r

r x y r r x y r

r x y r r x y r

» Fig. 3 Image charge method is applied for the chamber boundaries

Fig. 4. The contour plot representation of the potential and magnetic fields (V= 1 kV ve I=107 A).

There exists a perfect symmetry around the rods which enables to accelerate the ions in a symmetric force field. It is important, especially at higher voltages, because any asymmetry in potential field can cause an instability in the chamber and it directly affects the confinement.

Fig. 5. The contour plot representation ion trajectories at =-50 kV, B0=0.073 T » The interactions among the other ions

cause sudden chances in the directions of ions.

» Due to high energy, ions can accelerate through the walls.

Fig. 6. The position components of 5 electrons in the chamber. =-15 kV, Bo= 0.073 T. » Electrons can have high frequency

fluctuations in especially x-direction at the center due to the interactions with other particles.

Fig. 7. velocity components of a a single electron. =-150 kV, Bo= 7.3 T. » Electrons can have high velocities. For

high velocities in -z direction, they are attracted towards the central region.

Fig. 8. Trajecctories of 3 electrons for a small time duration. Parameters are =-150 kV, B0=0.073 T.

» 3 electrons are repelled from each other due to the Coulomb interaction. They also move far from the cathode rod.

Fig. 9. The position components of a sample ion in the chamber.V=-15 kV, Bo= 0.073 T

Ions have much mobility in x and y directions, however it has constant z value due to the magnetic field, since B enforces the ions at the bottom of chamber. Although ion position sdo not fluctuate at high frequencies as in the case of electrons, they still have have vibrations inside the central region. The velocities also fluctuate with lower frequencies due to ion mass.

Fig. 11. The positions of ions (blue) and electrons (red) at t=3.04s.

Fig. 10. The velocity components of a sample ion. =-150 kV, Bo= 7.3 T

Fig. 12. Ion temperature as function of time. 20 ions are used for tests.

Fig. 13. Ion temperature as function of time. 300 ions are used for tests.

Fig. 14. Energy spectra of ions. 300 ions are used. Parameters are =-150kV, B0=0 T, rc=0.2 m.

Fig. 15. Velocity spectra of ions. 300 ions are used. Parameters are =-150kV, B0=0 T, rc=0.2 m.

» Average reaction rate formula

» D-D reaction cross section has been found as, log(<v>)=-29.7219 » It corresponds to <v>= 1.89x10-30 m3/s

» From Fig. 14, T=35 keV is used for the formula. » Ion density is taken as the averaged value from Fig. 16(b) n= 1016 m-3

» The averaged velocity is taken as v=2x106 m/s from Fig. 15. » Thus, the number of reaction, dN/dt= n<v>=1.89x10-30x1016=1.89x10-14s-1

» Neutron rate, NPR= 1.89 x 10-14 x 3.14x 1019 =5.96x 105 n/s for the pressure p=0.13 Pa.

Fig. 16. (a)Position distribution of ions and (b) ion density. Parameters are =-150kV, B0=0 T, rc=0.2 m.

Fig. 17. Horizontal positions of ions and electrons. Parameters are =-150kV, B0=0 T, rc=0.2 m.

» A new IEC device has been designed.

» The new design uses the many body approach together with the FDM.

» The model includes the magnetic excitation steming from the central current wire.

» The model includes electron-ion, electron-cathode, ion-cathode, ion-ion and electron-electron interactions.

» The trajectories of electrons reflect higher mobility with much fluctuations.

» Ion trajectories exhibit fluctuations at the center and make helical trajectories.

» Neutron rate has been found as 5.96x 105 n/s.

» The averaged ion velocity has been measured as v=2x106 m/s.

» The averaged ion energy is found to be 30 KeV from the simulations, however there exist highly-energetic ions upto 700 KeV.

» The particle number should be increased further.

» The behavior at higher magnetic field should be examined.

» Longer measurement of temperature should be performed.

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[16] B. Dursun and E. Kurt (2014). Electromagnetic Design and Simulation of a New Fusion Device. Elektronika ir Elektrotechnika , 20(8)(34-38).

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