We don't work around conservation laws.
Ionizing atoms, or separating electrons from nuclei or atoms (which become ions) is like pulling springs (increase in mechanical potential energy) or lifting something in a gravity field (increase in gravitational potential energy). A force must be applied over a distance, and the energy applied is equal to the integral of the force over that distance.
So, one needs to add energy to a system from outside the system to increase the potential energy.
Stored chemical energy simply means that somewhere energy was added to chemicals to change their state, e.g. fossil fuels used to be organic material which transformed water and CO2 into sugar, cellulose and other organic compounds. Then when the plants died, they decayed, and were subsequently covered with rock and other minerals. Over 10's or 100's of millions of years, they were transformed into gas (methane, ethane), petroleum, and coal. Fossil fuels are simply chemically stored solar energy.
Similarly elements (atoms) were created billions of years ago and most are not in their lowest energy configuration. Stars transform hydrogen into helium over long periods of time. Stellar nucleosynthesis in some cases produces the heaviest elements, e.g. thorium, uranium, plutonium, which then may collect in planets. The Th and U in nature were created billions of years ago, and they represent nuclear potential energy, which we can release in nuclear reactors.
So energy in our systems must be added.
The remaining issue is that left to itself (in the absence of magentic fields or energy), the plasma neutralizes itself since electrons will search out positive charges via the Coulomb attraction.