Hi Philbo.
I'm planning on creating a topic to explain the fundamentals of Ambisonics and your question here is one of those I plan to address with that topic.
For now though, basically first order Ambisonics is akin to combining three m/s techniques into one recording. A first order Ambisonic recording contains four audio channels. They are known as W, X, Y and Z. This is also commonly referred to as B-format.
As you no doubt know, with a regular m/s recording, we have either a cardioid and figure 8 mic or an omni and figure 8. The omni gives us a mono signal and the figure 8 gives us the sides which when combined during m/s decoding, creates a stereo field.
In Ambisonics, a complete first order configuration gives us an omni (W channel), a front/back figure 8 (the X signal), a left/right figure 8 (the Y signal) and an up/down figure 8 (the Z signal).
When decoded, these four channels give us a full 3D sound field with depth, width and height information.
The sound field resolution is determined by the Ambisonic order. First order gives us one lobe per direction and the lowest spacial resolution. As we increase the Ambisonic order, we add more channels which basically split the lobes into smaller lobes which gives us increasing spacial resolution. This is also referred to as spherical harmonics.
A second order Ambisonic signal has nine audio channels instead of four and a third order signal has sixteen channels. They all still contain the basic mono omni (W) channel but add to the complexity of the spherical harmonics (the lobes in each direction) using pre determined mathematical formulae. The extra channels in each increasing order contain additional spacial information and greatly increase the ability for the listener to perceive accurate spacial cues.
REAPER is ideal for higher order Ambisonics because it can have up to 64 audio channels per track which equates to seventh order Ambisonics. The free IEM plugin suite mentioned in various posts here supports up to seventh order Ambisonics and the man in charge of IEM development, Daniel Rudrich, is a member and contributor here as well.
This is the IEM website..
https://plugins.iem.at/