How does a plasma lamp work?

Answer 1

Well, it is certainly not a globe with just electrons glowing inside it!

The globe contains a very hot ionized gas, which is known as a plasma.

A plasma is defined as:

An electrically neutral, highly ionized gas composed of ions, electrons, and neutral particles. It is a phase of matter distinct from solids, liquids, and normal gases.

Answer 2

A special physical feature is exploited in halogen lamps: when small amounts of a halogen gas were added to the contents of the light bulb, these were found to help to return large quantities of evaporated tungsten atoms back to the filament.

This treatment results in a significantly longer lifetime of such lamps.

Additionally it has the benefit that halogen light bulbs can be operated at a higher temperature than can be used for ordinary light bulbs. This results in less heat production compared to light output and an overall much higher efficiency in the conversion of the energy input (electrical energy) to the energy output as light.

General note about how all incandescent filament light bulbs operate

An electrical current travelling through the filament of a light bulb makes it glow white-hot and generate both light and heat because of the electrical resistance of the filament.

The filament is normally mounted within a special mixture of noble and/or inert gases held inside the glass enclosure of the light bulb, held at a pressure which is close to a vacuum.

The special mixture of gases prevents the filament from oxidizing and burning away, which would happen extremely quickly if it glowed white-hot in normal air which contains oxygen.
A halogen lightbulb uses a material called tungsten. The tungsten is in a gas filled bulb, but the pressure is higher than a regular lightbub. The reason for this is that the halogen lightbulb has a much smaller area than the other type. The trouble with this is that they can get very hot, making them almost dangerous to touch while on.