Many books on plasma physics (Chen, Goldston, Lieberman) say that quasineutrality must be satisfied for the matter in question to be a plasma. Yet, we know that non-neutral plasmas exist. So why do so many books make this claim?
Answer
In the old days, most plasmas were created with discharges in gases or such. This can stay a plasma for a long time (at least seconds). If it were not quasi-neutral, the accumulated charge would strongly pull ions away from electrons and make the plasmas explode. That's why books make this claim, and it is still true in many cases.
Nowadays, plasmas can be created in ways that the explosion time is larger than the time it takes to create it. For example, you can create plasmas in less than a picosecond with lasers, and these plasmas may be non-neutral.
Another way is to confine a non-neutral plasma with electric and magnetic fields.
Note that some people like to call plasmas only neutral ones, or even call them plasmas only when it is fully ionized. It is just a matter of definition, and old books can be confusing.
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