Can an ion beam be strong enough to create a path for lightning to travel to the ion machine?
This is what I found in a lab that may help: An ionization factor jτi (the product of electron beam density by the time of bombarding a stationary ion target with the electrons) approximately equal to 1.5 × 102 2 cm-2 has been achieved at an electron energy of Ee = 20 keV. This allows one to produce rather highly charged ions including argon nuclei (Ar18+) and He-like ions of krypton (Kr34+) and xenon (Xe52+).
Answer
Actually it is a relatively aged topic and it is still ongoing research area and is called "Laser induced discharge". In this technique that has a lot of details and unknowns, a laser pulse, which is usually shorter than picoseconds, ionizes the air molecules, so the ions make a trail to initiate the lightning. In the figure
an arc between two electrodes in the lab is shown. The left image shows the discharge without laser and the right image is discharge induced by the laser pulse (the bright narrow horizontal line close to the top electrode is the laser beam). Note how the almost random and fuzzy shape of discharge channel in left is directed by laser in right image. Other example is this figure:
in which the top image is the discharge between two electrodes without laser pulse and the bottom is the laser induced discharge. Usually in such experiments without presence of the laser the voltage between electrodes is lower than the voltage required for the discharge to get triggered. This is why they call it "laser induced discharge". With this technique, then, you can direct the energy of lightning and trigger it as well. You can shoot laser beam to kilometer distances, while the ion beams are limited near the source.
These experiments have a long-term goal to harness the lightning energy, however, the research is trying to defeat some obstacles.
For more info see the paper below and references therein: Large scale Tesla coil guided discharges initiated by femtosecond laser filamentation in air Arantchouk, L. and Point, G. and Brelet, Y. and Prade, B. and Carbonnel, J. and André, Y.-B. and Mysyrowicz, A. and Houard, A., Journal of Applied Physics, 116, 013303 (2014), DOI:http://dx.doi.org/10.1063/1.4886582
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