Reply To: Military Effects

[Joseph Chikva]

And it is proposed to create orthogonally to equatorial plane of vacuum chamber the bending magnetic field penetrating only its curvilinear segments. Such a field may be created by dipole magnets like to how similar purpose fields are created in synchrotrons or by betatron type magnet systems. The order of initial value of that field would be 0.1-0.4T. Then in the course of acceleration field’s induction should be increased correspondently to instant momentums of maintaining particles, thus keeping comparatively constant equilibrium radius.

To apply axial (toroidal) magnetic field only in the regions located remotely from injection points
Periodic axial magnetic field is needed for avoiding or slowing down of instabilities (e.g. two-stream instability)
As it is shown in number of papers [e.g. 9] that such a field dramatically expands stability area.
Beams injection points should be free from influence of that field but being injected particles should pass through that field in each turn.

To inject into the common axis (axis of vacuum chamber) 3 (three) pulse high current beams.
It is offered to inject two beams of particles of reacting components and to direct them along the same orbit and at the same direction but with different coherent motion velocities.
So, one faster ion beam should transit (pass) through another slower ion beam and their relative velocity should be sufficient for providing to reacting nuclei enough collision energy required for fusion (enough energy for Coulomb barrier overcoming).
For achievement of sufficient intensity of nuclear fusion the focusing of reacting beams is necessary. For this purpose it is offered to direct the relativistic electrons beam along the same orbit but towards (oppositely) to reacting particles beams.
This relativistic electron beam should compensate the positive space charge only partially and at the same time thanks to the magnetic attraction of combined three beams (three unidirectional currents) will compress the whole system in radial direction (pinch-effect). In fact pinch-effect will be provided thanks to the circumstance that in frame of reference connected with ions combined beam will charged negatively and for frame of reference connected with electrons – positively.
In the first approximation (not taking into consideration self-fields and influence of walls) the condition for beams for moving along the same equilibrium orbit is equality of gyroradiuses of particles.

Gyroradius can be calculated by the formula:

(1),
Where:
rg – gyroradius of particle
q – charge
B – induction of bending field
And equality of gyroradiuses for equally charged particles (e.g. deuterium, tritium and electron) means that their coherent motion momentums should be equal.

And e.g. for:
• Deuterium – 450keV
• Tritium – 300keV
• Electron – 40.6MeV
all momentums are equal to ~2.2*10-20 kg*m/s and at Bb=0.1T

rg=~1.4m

Deutrons 450keV and Tritons 300keV moving along the same axis at the same direction have center-of-mass collision energy ~30keV.
Such an energy provides rather high fusion cross section equal to ~1barn

G.I.Budker [1] says about achievability of order of magnitude of number density in such beams of 1026m-3 and even higher and beam’s radius of fractions of mm. Generally radial dimension of combined beam is a function of circulating currents, positive space charge neutralization level, coherent velocities of ions, relativistic factor γe and temperature. And varying with electron current for a given ion currents we can easily control the radius of combined beam.

For a given above sample of particles’ energies:
• γe=80.5 (relativistic factor of electrons in fixed frame of reference)
• γt=81.6 (relativistic factor of electrons in frame of reference connected with tritium)
• γd=82.2 (relativistic factor of electrons in frame of reference connected with deuterium)
And if nd=nt=ni/2, condition of pinch (excess of magnetic attraction forces on space charge repulse forces) will be:

ne>1/3355ni

So, the combined beam may be dramatically non-neutral and nevertheless suffering pinching. And this circumstance would be salutary for energy balance.

Injection challenge
Injection into vacuum chamber of very high current beams is a challenge. As the currents of thousands Amperes order for electron beam and tens/hundred thousand Amperes for ions are required. And such beams are space charge dominated.
But induction electron accelerators (Induction Linacs) produce rather high quality beams (energy spread <1%) and, so, having narrow phase volume (space), radius of vacuum chamber would have 0.5-2m order, while electron beam’s radius before injection – ~0.15m and electrons will be high relativistic 40.6MeV (γe=80.5, repulse forces reduce by factor of 1/γ2).
And commonly the injection of intense relativistic electron beams is well developed in number of laboratories [3] Fig. 1
And if we would inject firstly the electron beam and that then will totally fill the whole circumference (along axis) of chamber, the rather deep potential well for positively charged particles will be created, the depth of which is equal to [2]:

W=ve(1+2ln(R/Re)mec2 (2),

Where:
ve – Budker’s parameter ve = Ne2/m0c2 N-linear density (for Ie=4kA ve=0.235)
R – radius of vacuum chamber
Re – radius of electron beam
And for Ie=4kA, R=0.75m, Re=0.113m (je=10A/cm2)

W=1.123*mec2=574keV

And 574keV is rather enough depth for effective injecting into the same space ions producing by ion diodes even despite the fact that they have high energy spread and, so, big phase space.
Energies of ions:
Deuterium – 450keV
Tritium – 300keV