As I have found out that I will have a wider area (4' x 8') in that Poster Session, I also added the chapter on instabilities there.
Instabilities
In spite of the fact that mag field configuration of proposed Concept is very similar to TOKAMAK (combination of toroidal
and poloidal fields), stability limits written for TOKAMAK (Kruskal-Shafranov, Troyon, etc) are not quite applicable
As:
- Plasma is quazineutral in TOKAMAK unlike the Concept
- There are not high relativistic electrons in TOKAMAK unlike the Concept
- Bremsstrahlung is not considered as one of stabilizing factors in TOKAMAK unlike the Concept
- Temperature in a beam by the Concept is at least on order of magnitude lower than in TOKAMAK
- Etc.
Kink Instability
Electron component is high relativistic and it is well known that in case when v<<γ beam does not suffer kink instability even without usage of external stabilizing factors (such as axial mag field, conductive wall, etc.). And electron beam provides some “rigidity” to the combined beam.
Here:
v = Ne^2/m0c^2 is so called Budker’s parameter in which N is the number of electrons per unit of length
( v = 1 corresponds to case when N = 3.6E14 m^-1 and electron current equal to 17’000 A)
On the contrary, ionic component has a high v with γ close to 1 (v > 1), produces strong poloidal mag field at the surface and should be stabilized from externally. But the fact that ions move along the axis and in potential well of “rigid” electron beam together with the stabilizing factor of comparatively weak toroidal field allows to hope on immunity against on at least short wave kink instability.
Long wave kink instability can be eliminated by electrostatic quadrupoles (usage of such quadrupoles is proposed also for HIF)
Transverse Instabilities
Transverse Instabilities such as:
- Betatron waves
- Beam breakup instability
- Transverse resistive wall instability
- Hose instability
- Etc.
may be damped effectively as something like “friction” is observed in combined beam.
Radiative “friction” by which via collective momentum interchanging all charged particles having transverse velocities moving in a very strong poloidal mag field dissipate energy via Bremsstrahlung
Longitudinal Instabilities
Longitudinal Instabilities such as:
- Two-stream instability
- Negative mass instability
- Longitudinal resistive wall instability
- Etc.
can not be dumped effectively only by radiative “friction”.
But also it is well known high relativistic factor slows
two-stream instability’s development rate and there are number of papers in which is stated that comparatively weak longitudinal mag field dramatically expands stability area.
So, proposed concept will have immunity on at least electron-ion two-stream instability, electro-electron two-stream instability will not be observed at all and ion-ion due to ions’ lower charge-to-mass ratio are less subject to this type of instability.
Also for ion-ion two stabilizing factors:
- Longitudinal mag field
- Certain initial spread of ions' velocities
would be useful.
Negative mass instability should not be a problem for proposed Concept due to the fact that despite of non-neutral nature of combined beam, nevertheless ions are in negative potential well of electrons and electrons – in positive potential well. And there are not conditions for grow of this type of instability in this case.
Regarding
Longitudinal resistive wall instability: its growth or damping depends sensitively on the axial velocity distribution of particles near the phase velocity (when damps - Landau damping). And by Neil and Sessler the rule for stability here is that the spread in circulation frequency must be near the certain value.