Let me see if I can simplify the explaination.
The basic concept is really pretty simple.
The blade is nothing more than an electrical spark (arc). Very much like what you get when you create a spark between two wires, using a transformer, or even a battery. It is an unusual spark, but just a spark.
We know that the higher the voltage, the longer the spark we can make. So we calculate the length of spark we would need, and design a generator to produce the voltage needed.
At this point, its still just a spark, not a lightsaber blade.
To get it to act like a lightsaber blade, we have to first increase the frequency of the current supply. When we reach a high enough frequency, the arc takes on the properties we are looking for. At the high frequencies we need, the arc is no longer just a gaseous plasma. It becomes 'solid' and 'hard', from the point of view of its physical properties. It's the high frequencies that give the spark the 'solidity' and 'hardness'. We are really just turning the current on and off super, super fast, in a certain way.
There is no containment field. The arc maintains itself, it holds itself together, there is no need to contain it.
Each individual ion (charged particle) in the blade is held to the others in a manner similar to the way magnets hold onto each other. The blade does not need a containment field, and does not have one.
We do need to shape it, though, otherwise we would just have our 'solid' arc zipping between two electrodes.
The magnetic mirror does nothing more than push the arc out into a blade shape.
This is possible because we spin the arc, in exactly the same way a rotor spins in an electric motor, with a rotating electromagnetic field. The magnetic field is only needed to spin the arc, not to contain it. In fact, the arc is generating its own magnetic field, which pushes it away from the magnetic mirror (through reflection - like polarities repell each other), out into the blade shape.
It's just a very special kind of shaped and spinning electrical spark. Extremely high voltage and frequency. It's not made of light, although it emits light. It's made of a sort of condensed super plasma, which contains itself.
Does that help?