J. Plasma Fusion Res. SERIES, Vol.3 (2000) 211-213

Magnetic Suppression Concept for Secondary Emission
Electron End Flux in Open Systems
KHVESYUK Vladimir I.*, CHIRKOV Alexei Yu. and BADIKOV Denis N.
Bauman Moscow State Technical University,

Power Engineering Institute, P.O. Box 38, Moscow, 107005, Russia(Received: 18 January 2000 / Accepted: 8 March 2000)

Abstract
The electron temperature in a mirror plasma is sufficiently lower then ion temperature. The mostprobable reason for this effect is the influence of relatively cold secondary emission electrons penetrating

into the plasma along open magnetic lines. The principle of decreasing of secondary emission electron
flux for a mirror configurations is suggested. In correspondence with the idea of the principle ends ofopen magnetic lines should be curved. It is shown that particle drift in curved magnetic field leads toreducing particle fluxes along lines, and the value ofcold secondary emission electrons penetrating into
plasma core decreases in this case.

Keywords:
tandem mirror, open lines, secondary emission electrons, toroidal end cells

1. lntroduction

in comparison with ion temperature [3]. The study of

The tandem mirror confinement system is very
attractive from the viewpoint of creation steady statefusion reactor because it has following advanced

potential formation [4,5] showed that the most probablereason of this phenomenon is the cooling of electroncomponent by relatively cold secondary electrons

features:emitted from the surface of chamber wall due tol) simple geometry;interactions with particles (ions and electrons) lost fromthe central cell along open magnetic field lines [4,5].
Secondary emission (SE) of electrons from metallic
surfaces ofends ofthe system leads to additional power

2) possibility of steady state operating;3) possibility of high-p confinement;
4) possibility of using direct energy conversion sys-losses from plasma due to cooling effect of SE
electrons, and limitation of electron temperature. Thissituation limits fusion prospects of the tandem mirror.
To provide better power characteristics needed forsteady state operating it is necessary to reduce the effecttemst etc.

The features 3 and 4 are especially important for prospects of low-radioactive fusion reactor using D-3He fuel[,2] because for high efficiency D-3He fusion B > 0.5 isneeded, and the major value of fusion energy in D-rHeof cooling of the tandem mirror plasma by SE electrons.
The main goal of this work is to consider possible
simple modifications of the tandem mirror confinement
system possibilities of reducing SE effect. In this work
we consider method of plasma insulation by curving

cycle is associated with charged particles.

Tandem mirror experiments showed one
disadvantage of this system is low value of the electrontemperature.

Experiments on GAMMA-I0 tandem mirror
showed electron temperature had sufficiently low value@2000 by The Japan Society of Plasma
Science and Nuclear Fusion Research*Corresponding author's e-mail: khves@ power.bmstu.ru

2rl

Khvesyuk V.I. et al., Magnetic Suppression Concept for Secondary Emission Electron End Flux in Open Systems
centralcellbarrier cell

'1 .---/1.

end plates

device.

In the tandem mirror SE of electrons from the end
plates appears due to the influence of ions and electronsIIlost from the central cell of the tandem mirror alongopen magnetic field lines. The scheme illustrating thisphenomenon and distributions of magnetic field andt,, I

electrostatic potential along the magnetic axis ispresented in Fig. l. The SE electrons penetrate into theplasma along and cool it.

The flux of SE electrons into the plasma grows
with the growing of particle flux from the plasma along
magnetic field lines. Consequently SE electron flux canbe reduced by decreasing of fluxes of ions and electrons

from the plasma. When ion flux from the plasma
decreases, electron flux decreases too, because of thesetwo fluxes are connected. Consequently decreasing ofion flux leads to decreasing of the total particle flux
Fig. 1 Diagram of magnetic field profile, electrostatic
potential and directions of trajectories of irons
and electrons in the tandem mirror.

central cellbanier#along magnetic field lines from the plasma. The methodof the decreasing of particle flux along magnetic fieldlines based on the effect of ions drift perpendicularly tomagnetic field vector in curved line magnetic field isconsidered in the next section.

cell toroidal end cell

3. Principle of SE Electrons EffectSuppression
In order to protect plasma from cold secondary
emission electrons, it is possible to close magnetic forcelines by the following method. Two "parallel" mirrors
can be linked by semi-toroidal cells. The more simple
method of reducing of SE electron flux due suppressionof parallel plasma particle flux is based on properties ofrecently suggested magnetic configuration with toroidal
ends [7]. We consider open configuration includes thetandem mirror and toroidal magnetic field cells installed\\\ \;i:d"Fig. 2 Scheme of magnetic field configuration of tandem
mirror with toroidal end cells.

on both ends of the tandem mirror. This magnetic
ends of field lines. The idea of such insulation is based

configuration is presented in Fig. 2.
In toroidal field ions drift in direction perpendicularon the effect of ions drift perpendicularly to magnetic
field vector in curved line magnetic field is consideredin the next section.

both magnetic field ,B and its gradient VB, andconsequently they leave plasma across the magnetic
field not along the open lines. This B x VB drift for ionsand electrons has opposite directions, that leads tocharge sharing and formation of electric field parallel tothe direction of B x VB drift, and consequently .E x Bappears. Joint action of these two drifts forced particles
leave plasma before they can achieve ands of thesystem. These particles can induce SE from the toroidal
wall of the toroidal end cells, but in this case theinfluence of the SE electrons in this case will belocalised in scrape-of layer. It means that SE electrons
will not penetrate into core plasma the central cell and2. Secondary Emission Electrons Problem inthe Tandem Mirror
The problem of SE electrons cooling plasma isactual for different confinement systems. For example,in tokamak the flux of secondary emission electrons into
plasma can be reduced using grids under positiveelectrostatic potential [61.

The main feature of considering problem fortandem mirror devices is the presence of open magnetic

field lines piercing the surface of the camber wall of the2t2

Khvesyuk V.I. et al., Magnetic Suppression Concept for Secondary Emission Electron End Flux in Open Systems0Fig. 3 Trajectories of particles in toroidal end cell. X-Y is the plane perpendicular to the toroidal field (on the left side ofeach figure), andY-Z is the equatorial plane of tore (the right side). Start points are marked by rounds. Crosses
mark points where particles achieve toroidal wall. Arrows show direction of the toroidal magnetic tield. 8",= 2T,

r*=0.5m,Fr=2m;a-e=0.1 keV,go=0;b-e=1keV,9o=0;c-e=1keV,0o=5';d-e=1kev,qo=20".

cool it sufficiently.

4. Conclusion

Efficiency of suggested insulation method can beillustrated by ions trajectories in toroidal cells.
Trajectories presented in Fig.3 where obtained as anumerical solutions of dynamics equation for particle
motion in model magnetic field of consideringparallel plasma flux on the wall of the ends of tandem
mirror can. Presented concept of suppression is based on
simple method of plasma insulation due to drift incurved-line magnetic field, and this method allows

It was shown the high efficiency reducing ofconfiguration with toroidal end cells. This calculations
were carried out neglecting the effect of the electricfield. We assume that the magnetic field value on themagnetic axis of toroidal freld Bo, is equal to the valueof magnetic field in the central cell. In Fig. 3 e is the ion
energy, 0s is the ion pitch angle in the central cell, thesizes of toroidal cell wall are Rr (the tore axis radius)and r* (the small radius of tore). The end cell toroidal
angular size for calculation was assumed to be 180', but
as one can see toroidal angle about 90o is can bereasonable for the insulation. Calculations showed that
presented insulation method has low efficiency for slow
ions (see Fig. 3a), and it has high efficiency for
relatively high-energy particles (see Fig. 3b-d).

simple technical realization.

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