*DC Parallel Ribbon Ion Beams for High-Dose Processes DOI: http://dx.doi.org/10.5772/intechopen.111487*

beam, but when I tried to transmit it through an analyzing magnet, the beam blew up, even in the space before entering the analyzer magnet. The ribbon beam source I was using, like that in the NV10 implanter, had a slightly concave front aperture from which the beam was extracted, with the electrodes shaped to be parallel to this curve, so that the beam converged in the breadth dimension. The universally held belief (despite the Calutron experience) was that a magnetic field helped space-charge neutralization, but our observation was that the magnetic field could disrupt it. We could turn the magnet on and off, and watch the magnetic field cause the disruption of the beam exiting the ion source and entering the magnet. We made Langmuir probe measurements of electron temperature in the space very close to the beam, and we observed that applying the magnetic field to the beam could trigger a dramatic increase in electron temperature.

Analysis of the beam size, current density, perveance etc., and the application of some standard plasma science, led us to hypothesize that under certain conditions, unstable ion sound waves could be transmitted through the plasma within the ion beam. We never saw the beam blowup below a certain threshold current, but blowup would occur suddenly as the magnetic field was raised, only when certain quantifiable conditions were met, namely that the ion plasma frequency, Ωpi exceeded the ion cyclotron frequency, Ωc, by a significant factor, of the order of 2.

$$
\Omega\_{\rm c} = \frac{qB}{M} \tag{3}
$$

$$\mathfrak{Q}\_{pi} = q \sqrt{\frac{n\_i}{\varepsilon\_0 M}}\tag{4}$$

The cyclotron frequency in ion implanters is typically in the range from 200 kHz to 1 MHz, and when beam blowup is observed it is accompanied by chaotic hash on the beam at frequencies above this threshold. Note, however, that ni in Eq. (4), the density of ions, is not a well-defined quantity, as there are several ion populations present, whose interaction is not straightforward.

$$n\_i = n\_b + n\_r \tag{5}$$

where nb is the density of ions in the beam (not uniform) and nr is the density of slow ions generated from the residual gas.

$$m\_b = J\_b \sqrt{\frac{M}{2qV}}\tag{6}$$

The slow ion density nr is very difficult to evaluate, as it is proportional to the pressure, the beam current density, and the local potential distribution, since these positive ions will be weakly accelerated away from the beam center; the potential distribution is affected by the electron temperature, so nr will drop as soon as the beam neutralization is perturbed. The pressure is usually related to the beam current and to geometric factors, and is rarely well-known in the center of a magnet.

$$n\_r = \frac{I\_b n\_0 \sigma}{2(t\_b + b\_b)v\_i q} \tag{7}$$

where tb and bb represent the beam thickness and breadth within the magnet, vi is the velocity of the slow ions as they are repelled from the beam by its plasma potential, n0 is the residual gas density, and σ is the total cross section for slow ion generation by the beam. To further complicate the picture, the beam ions contain multiple species, and Alexeff [6] showed that this can create additional instabilities. The beam ions are traveling at supersonic speed in the plasma. White and Gray Morgan presented a paper [7] in the form of a poster at the IEEE Plasma Science conference of 1991, in which scaling with the background gas ion density was demonstrated, and discussions with other participants including Igor Alexeff, founder of IEEE Plasma Science division, established that our scaling law was consistent with his models [6], and further that the geometry we were using could function in a similar manner to a klystron, and amplify the instabilities with self-feedback. When the ion density fell below the threshold we describe, the beam was stable.
