We know that in nature there are many visible plasmas around us, as fire, candle flame, aurora, etc. But what about plasmas that emit light out of the visible light range. Does exist this kind of plasmas? If so, are there concrete examples?
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But what about plasmas that emit light out of the visible light range
All hot things (temperature $T>0$), emit light in and out of the visible range. It's just that we can only see the visible part of the emission and that the intensity of emitted light may not peak in the visible band.
Plasmas are hot - in true plasmas, atoms have been completely reduced to ions. These of course emit light beyond the visible region too - some most intensely so. However, they most likely emit energy in the visible region too. So hot plasmas are almost always visible. For example, plasma at fusion temperatures (star core, nuclear fireball) emits tons of radiation not in the visible region.
Partially ionized plasmas on the other hand may or may not emit light in the visible region while emitting light in other frequencies. For example, the vapour discharge of an ionized gas (in tubelights, CFLs, neon signs). These are best candidates for "invisible" plasma.
