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Psi is an abbreviation that represents parapsychological phenomena collectively. Parapsychology is the "study of mental phenonmena outside the sphere of ordinary psychology".(The Oxford English Reference Dictionary) Telepathy, telekinesis,ghosts, hypnotism, and energy work would more or less fall under the parapsychology umbrella.
Few dictionaries carry a definition of psionics, but basically it involves working with and manipulating energy. It should be noted that psy vampire is merely a vampire who is psychic. Psy is the abbreviated form of psychic. People often confuse the psi and psy, they are often related, but not the same thing. A sanguinarian vampire could be psychic for example, but not a psi vampire.
A psi vampire is someone who requires pranic or life force energy from other sources in order to maintain good health. There is no evidence to suggest that vampires who do not feed will die, it is not as melodramatic as all that. In addition to feeding off of the energy of living things, some psi vampires can feed off of the earth such as nature or storms, and sometimes even power sources. Psi vampires do not need to be around people all the time. They do not need to feed constantly - just like everyone else does not need to eat constantly to meet their energy requirements. Some psi vampires feed on excess energy present in large groups like at shopping malls or at a concert. Others prefer to feed on individuals, and some do so with or without their permission.
In order to understand psi vampirism there is perhaps one example that makes it very simple. Almost everyone knows someone who is difficult to be around because after you have interacted with them you feel rather depressed and down, and quite drained. You don't feel happy or energized after your time with them. A lot of such people have constant drama and their demands on you for emotional support can sometimes tap into your energy reserves because they take and do not give back. Such people are often depressed individuals but they are not always vampires. This is just an example I use to help people understand the concept of psi vampirism. It does not mean that all psionic vampires have this affect on people, nor does it suggest the people who make you feel "drained" are vampires. Such people are not definitions of psi vampirism though, I was just using the concept to illustrate what is possible. It makes the possibility that someone can feed on energy a little more understandable. However, it is not something that is supernatural. I think it is something natural that has not been explored overly much in the world of science.
The person being fed off may or may not feel anything. If they do feel something it is usually a feeling of fatigue or tiredness. Individuals who are more sensitive may sense that something "strange" is happening but they don't know what. Fully awakened individuals(not just vampires, but any "aware" person) may know exactly what is happening. Skilled psi vampires may make the feeding quite pleasant for the donor because they can take some energy and then give it back. Not everyone would practice this kind of cycling though.
Some people believe that a vampire is a vampire, in other words, there is no difference between a sanguinarian vampire and a psi vampire. The difference lies in the method of getting the energy - the sanguinarian gets pranic energy from the blood, whereas the psi vampire gets it without using the blood as a "vehicle". There is quite the debate about this issue as some sanguinarians insist they cannot feed without getting the blood. There is the opinion that they can get the energy without blood but they have blocked that ability and are holding themselves back. It does not look like this particular debate will be resolved any time soon.
There are many approaches and ideas in terms of psi vampirsm so the the information presented here is a general overview. For more information on psi vampirism, please visit SphynxCatVP's site.