1. PLASMA HEATING AND HOT ION SUSTAINING IN MIRROR BASED HYBRIDS
V.E.Moiseenko1,2, O.Ågren2,
1 Kharkiv Institute of Physics and Technology, Ukraine
2 Uppsala University, Sweden

2. OUTLINE SFLM AND STELLARATOR-MIRROR FDS SCENARIOS FOR NEUTRON SOURCE
NUMERICAL MODEL FOR NBI
CALCULATION RESULTS FOR NBI
SCENARIOS FOR ICRH
NUMERICAL MODEL FOT ICRH
CALCULATION RESULTS FOR ICRH
CONCLUSIONS

3. SFLM AND STELLARATOR-MIRROR FDS
Usage of a open trap for hot ion confinement is beneficial to localize the fusion neutron flux to the SFLM part of the device which is surrounded by a fission mantle.
The devices would be capable to operate continuously.
It is expected that full control on plasma could be achieved.

4. SCENARIOS FOR NEUTRON SOURCE
Two scenarios of discharge arrangement in mirrors are of interest for the fusion neutron source. Both take advantage of mirror trapping of high energy ions.
In the first scenario one ion component is hot, and neutrons are produced in collisions with the background plasma ions which are in thermal equilibrium with the electrons.
In this scenario the power balance is determined by the electron drag: The power PTe-3/2 for the ion heating decreases with an increase of the electron temperature.
Additional heating of electrons, e.g. with electron cyclotron heating, is less practical because electron heating could be achieved by increasing the hot ion population, which also increases the fusion neutron output.
In the second scenario, both deuterium and tritium ions are hot.
The background plasma is sustained to stabilize plasma instabilities caused by the non-equilibrium (loss-cone) velocity distributions of the hot ions.
Here, the role of the electrons in power balance is less accentuated, and electron heating would be less important.
A key problem for the two mentioned scenarios of discharge is hot ion sustaining. This could be made with neutral beam injection (NBI) or radio-frequency (RF) heating in the ion cyclotron range of frequencies.

5. NUMERICAL MODEL FOR NBI
In the model it is assumed that the hot ions are in minority and collisions of hot ions with themselves are ignored.
Another assumption is smallness of the particle drift excursion in perpendicular to the magnetic field direction during collision time.
This assumption allows one to consider velocity distributions separately at each magnetic field line and ignore particle perpendicular motion.
The stationary kinetic equation for fast ions reads:
For Maxwellian plasma the collision operator is
and
indices hi and =e,i denote hot ions, electrons and background ions respectively .

6. NUMERICAL MODEL (cont.)
If (collision time)/(bounce time)>>1
New variables :
Bounce averaging
In the code, time is expressed in units of ion-ion collision time for the background ions. The velocity is normalized by the background ion thermal velocity.

7. CALCULATION RESULTS Regular parameter set:
magnetic field depends parabolically on the longitudinal coordinate
the mirror ratio is chosen as R=1.7, NBI generates ions with perpendicular energy at R=1.3. NBI energy spread is chosen as
For this parameter set the average normalized ion energy is
The electron drag takes 62% of the injected power, the ion-ion collisions 19%. The remainder goes to the loss cone and is lost due to finite confinement time at the mirror part of the device.
A change of the mirror ratio from R=1.7 to R=2 increases the hot ion content only by 1%, and the mean ion energy also remains almost unchanged.
Contours of distribution function. Dashed line shows boundary between trapped and passing particles.

8. CALCULATION RESULTS (cont.)
An increase of the ion confinement time at the mirror part from to
results in a hot ion density increase by 10%, and this value
does not change significantly with further increase of this parameter.
Confining properties of the stellarator are also not very sensitive: A decrease of the stellarator confinement time from to
results only in a decrease of hot ion population by 4%.
Neutron emission line intensity for Einj=300keV and two different background plasma temperatures.
If the fission mantle is located at |l|<0.5, the relative portion of the neutrons emitted in this zone is 61% for T=3 keV and 57% for T=0.8 keV.
If -0.5<l<1 this portion rises to 80%
Dependence of fusion Q on background plasma temperature for two normalized injection energies.

9. SCENARIOS FOR ICRH
RF field forms a standing wave in radial direction and propagates along magnetic field towards midplane
Minority heating:
Wave is launched by antenna near cut-off
Wave does not propagates to high field side reflecting from cut-off
FMSW then converts to FAW
Alfven resonances are also excited
FAW is absorbed owing to cyclotron damping
Second harmonic heating:
The same, but no conversion to FAW and no Alfven resonances
Conversion to IBW is possible
V.E. MOISEENKO, O. AGREN, Phys. Plasmas 12, ID (2005).
V.E. MOISEENKO, O. AGREN, Phys. Plasmas 14, ID (2007).

10. Scenarios for ICRH (cont.)
Second harmonic calculation
Reactor
Neutron source
Power
Re Ex
Im Ex
Re Ey
Im Ey
The SFLM neutron source has a substantially smaller size than a fusion reactor machine. In this situation the fast magnetosonic wave which is excited by the antenna makes fewer oscillations across the magnetic field.
The width of the ion cyclotron zone becomes smaller owing to the sharper gradients of the magnetic field magnitude along magnetic field lines.
The last factor is softened by a smaller mirror ratio.

11. NUMERICAL MODEL
Zero electron mass approximation is chosen in which the parallel component of the electric field is neglected in Maxwell’s operator
Boundary conditions
WKB formulas for cyclotron damping: fundamental harmonic ,
Second harmonic
V.E. MOISEENKO, O. AGREN, Phys. Plasmas 14, ID (2007).

12. PARAMETERS OF CALCULATIONS
Plasma radius at the central plane where the magnetic surfaces have a circular cross-section is a=40 cm, magnetic field value at the midplane is B0=2 T, the trap length is L=18 m and the mirror ratio at the trap ends is R=2.3.

13. CALCULATION RESULTS (MINORITY HEATING)
Dependence of the absorption (solid line) and shine-through (dashed line) resistances on RF heating frequency.
Dependence of the absorption and shine-through resistances on plasma density.

14. CALCULATION RESULTS (minority heating)
Dependence of the absorption and shine-through resistances on antenna location.

15. CALCULATION RESULTS (second harmonic heating)
Dependence of the absorption (solid line) and shine-through (dashed line) resistances on RF heating frequency.
Dependence of the absorption and shine-through resistances on plasma density.

16. CALCULATION RESULTS (second harmonic heating)
Dependence of the absorption and shine-through resistances on tritium thermal velocity.
Dependence of the absorption and shine-through resistances on antenna location.

17. CONCLUSIONS
Hot ion sustaining is most important for mirror and stellarator-mirror fission-fusion hybrid devices. Efficient methods for this are NBI and ion cyclotron resonance heating.
According to the numerical results for NBI in a stellarator-mirror hybrid, the hot ion population depends only weakly on the confinement of the stellarator part.
At the mirror part, it is sufficient to confine the hot ions for only a few hot ion-background ion collision times.
The mirror ratio of the local mirror trap which is sufficient to avoid substantial ion losses is small, a value R=1.7 is adequate, and increasing it does not result in a considerable increase of the hot ion population.
The calculated axial distribution of the neutron flux peaks at the injection points and has a noticeable magnitude at locations between the peaks. About 60% of the flux reaches the fission mantle if the NBI is made from both sides of the nuclear core. This amount rises to 80% for single-side NBI. It could be further increased by a steeper magnetic field profile near the injection area and making the field more uniform in the remaining mirror part.

18. CONCLUSIONS (cont.)
The calculations for the straight field line mirror hybrid show good performance of deuterium minority heating at the fundamental ion cyclotron frequency. The heating is not strongly dependent on the ion temperature and, therefore, has no start-up problem. The sensitivity to other factors, e.g. plasma density, antenna location etc., is not critical.
Second harmonic heating of tritium is always accompanied by a noticeable shine-through beyond the tritium second harmonic resonance zone. However, the wave power would not be wasted, since the shined-through wave encounters deuterium second harmonic cyclotron resonance on its way to the midplane. Most of the remaining small wave energy may also be absorbed at the tritium second harmonic resonance zone near the opposite mirror.
The second harmonic heating calculations predict relatively sensitive dependence on plasma density, antenna location and tritium temperature. However, if the necessary conditions are provided this heating is satisfactorily efficient.

19. Thank you!