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By and large the basic rules governing psychic powers/psionics are relatively unchanged from those on page of Rifts Ultimate Edition. Below are what changes or additions are applicable.
ISP boost at ley lines and ley line nexuses
The only change here is that you get a flat boost based on level of psychic you are.
Minor gets +2 per turn on a ley line and +4 on a nexus.
Major gets +3 per turn on a ley line and +6 on a nexus.
Master (Psychic OCCs) gets +5 per turn and +10 on a nexus.
As it says in RUE you must use this ISP right away and cannot store it for later use. (It essentially allows you to use powers at an ISP discount equal to the boost you get)
ISP Recovery
Typically you will regain 10% of your ISP per hour of restful sleep. (10 hours of sleep will regain all lost ISP if reduced to zero)
Proper meditation will increase this to 30% per hour.
Some OCC's may increase this rate.
Power Strength
This is similar to spell strength. This will increase the target number to save against as the character levels up in experience. Some psychics will not increase as much as other, much like different magic users increase their spell strength in different levels.
Base target to save against psychic abilities is 12.
Minor and Major Psychics get a +3 to save against psychic abilities. (These are the psychics that are not a class but added on by character generation chances)
Master Psychics (Psychic OCC's) typically get a +5 to save against psychic abilities unless noted otherwise in the OCC.
Increase in overall effectiveness
Unlike magic, psychics cannot "learn" how to increase the effectiveness their own innate abilities through tings like Foci....however most psychics, particularly master psychics, do see the effectiveness of their abilities increase innately as they go up in experience. Range, duration, damage, etc all increase over time as the psychic matures more and more into their powers.
This will differ from class to class and be detailed within each class just when and how their abilities increase in effectiveness.
NOTE - like spells and skills, many psychic powers will see revisions made to them.