Ionization
Ionization is the physical process of converting an atom or molecule into an ion by adding or removing charged particles such as electrons or other ions. This process works slightly differently depending on whether an ion with a positive or a negative electric charge is being produced. A positive electric charge is produced when an electron bond to an atom or molecule absorbs enough energy from an external source to escape from the electric potential barrier that originally confined it, where the amount of energy required is called the ionization potential. A negative electric charge is produced when a free electron collides with an atom and is subsequently caught inside the electric potential barrier, releasing any excess energy.
Ionization can generally be broken down into two types: sequential ionization and non-sequential ionization. In classical physics, only sequential ionization can take place and therefore refer to the Classical ionization section for more information. Non-sequential ionization violates several laws of classical physics and thus will be discussed in more detail in the Quantum ionization section.

# Classical ionization
Applying only classical physics and the Bohr model of the atom makes both atomic and molecular ionization entirely deterministic, that is every problem will always have a definite and computable answer. According to classical physics it is absolutely necessary that the energy of the electron exceeds the energy difference of the potential barrier it is trying to pass. Conceptually this idea should make sense: the same way a person can not jump over a one meter wall without jumping at least one meter off the ground, an electron can not get over a 13.6 eV potential barrier without at least 13.6 eV of energy.

## Applying to positive ionization
According to these two principles, the energy required to release an electron is strictly greater than or equal to the potential difference between the current bound atomic or molecular orbital and the highest possible orbital. If the energy absorbed exceeds this potential, then the electron is emitted as a free electron. Otherwise, the electron briefly enters an excited state until the energy absorbed is radiated out and the electron re-enters the lowest available state.

## Applying to negative ionization
Due to the shape of the potential barrier, according to these principles a free electron must have an energy greater than or equal to that of the potential barrier in order to make it over. If it has enough energy to do so, it will be bound to the lowest available energy state, and the remaining energy will be radiated away. If the electron does not have enough energy to surpass the potential barrier, then it is forced away by the electrostatic force, described by Coulombs Law, associated with the electric potential barrier.

## Sequential ionization
Sequential ionization is basically a description of how the ionization of an atom or molecule takes place. More specifically, it means that an ion with a +2 charge can only be created from an ion with a +1 charge or a +3 charge. That is, the numerical charge of an atom or molecule must change sequentially, always moving from one number to an adjacent, or sequential number.

# Quantum ionization
In quantum mechanics ionization can still happen classically where the electron has enough energy to make it over the potential barrier, but there is the additional possibility of tunnel ionization.

## Tunnel ionization
Tunnel ionization is ionization due to quantum tunneling. In classical ionization an electron must have enough energy to make it over the potential barrier, but quantum tunneling allows the electron simply to go through the potential barrier instead of going all the way over it because of the wave nature of the electron. The probability of an electron tunneling through the barrier drops off exponentially with the width of the potential barrier. Therefore, an electron with a higher energy can make it further up the potential barrier, leaving a much thinner barrier to tunnel through and thus a greater chance to do so.

## Non-sequential ionization
When the fact that the electric field of light is an alternating electric field is combined with tunnel ionization, the phenomenon of non-sequential ionization emerges. An electron that tunnels out from an atom or molecule may be sent right back in by the alternating field, at which point it can either recombine with the atom or molecule and release any excess energy, or it also has the chance to further ionize the atom or molecule through high energy collisions. This additional ionization is referred to as non-sequential ionization for two reasons: one, there is no order to how the second electron is removed, and two, an atom or molecule with a +2 charge can be created straight from an atom or molecule with a neutral charge, so the integer charges are not sequential.  Non-sequential ionization is often studied at lower laser-field intensities, since most ionization events are sequential when the ionization rate is high.