Newpic,
Roughly speaking, one can divide the range of a reversible, controllable propeller into two regions of operation; forward thrust, and reverse. Forward thrust, anything pushing or pulling the airplane in a forward direction, may be thought of as the "alpha" range, and anything that isn't alpha range may be thought of as "beta."
A propeller is an airfoil. It works by altering the pressure distribution around the propeller blade and the arc of the propeller. The propeller may be driven by the engine, and under some low power conditions when engine power is insufficient to motivate the propeller to move, it may be acted upon by another more powerful force, such as the slipstream as the airplane moves through the air; the slipstream may move the propeller. When the engine is driving the propeller this is referred to as positive torque; when the slipstream is driving the propeller this is referred to as low torque, zero torque, or in some cases, negative torque.
The alpha range of most reversible propellers allows the propeller blade to position itself to an angle which achieves what the pilot has commanded. The pilot does not set a blade angle, but tells the propeller what RPM to maintain, and the propeller does it automatically. In some engine installations such as the Garret TPE-331 or Allison T-56, the propeller turns at "100%" all the time. It's RPM is constant. The torque imparted by the engine is changed as the pilot moves the power levers; the engine temperature changes as fuel is applied or removed, and the engine tries to turn the propeller faster or slower...but the propeller won't allow it. What the propeller does do is change it's anglel in order to change the aerodynamic load it encounters, and thus keeps itself at a constant speed. When the engine temperature is increased by adding more fuel (and the engine tries to turn faster), the propeller blade angle of attack increases, and the drag on the prop also increases...the propeller RPM stays constant but thrust is increased. We call this the governing range...the range of movement of the propeller which allows it to do as commanded.
The propeller on many installations doesn't go to one speed and hold that speed. It holds whatever the pilot tells it to hold. When the propellers is going fast enough to start governing, the propeller governor will set and hold whatever speed the pilot tells it to hold. In the cockpit, the pilot moves a lever (which goes by several names depending on which aircraft and engine installation is in use) to set the propeller RPM. In so doing, the pilot is setting tension on a small spring inside the propeller governor, and the governor does the rest. It controls exactly what RPM is maintained by the propeller, and accordingly, the blade angle used to achieve that RPM.
The propeller itself deserves some thought. The part of the propeller facing the back of the airplane is actually the blade "face," or the part that equates to the lower surface of a wing. The blade is really an airfoil, much like a wing, generating "lift" if you will; downwash, and thrust, as it imparts energy to the air that passes through it. The blade is allowed to change the angle it meets the oncoming air; it changes it's "angle of attack." As the angle of attack changes, so does the drag or load on the propeller blade, and so does the amount of air it's moving and the way it's moved.
The propeller is restrained from moving too far, that is, increasing or decreasing it's angle of attack too much. It's restrained by stops, or pins inside the propeller assembly that block movement of the blade as it twists to increase or decrease the angle of attack (AoA). We call that changing the pitch of the blade. As pitch is increased to "coarse" or the high pitch/low RPM position, the blade face moves from facing the back of the airplane to actually facing sideways...the blade is aligned more with the slipstream...ultimately to what we sometimes refer to as the "feather" position. Some propellers automatically feather when the engine is shut down, and you can recognize them by looking at the propeller at rest from in front or behind the airplane. The blades look thin as they're rotated so the blade face is sideways, rather than facing the back of the airplane. The blade doesn't go that far in normal operations in flight, but you can get the idea of how the blade rotates. Understanding that rotation, from minimum drag/feathered/aligned with the slipstream, to it's high RPM/low pitch position...when the blade is in just the opposite position from feathered. In it's high RPM position, the blade fact, usually painted black, if facing the back of the airplane, and it's resting against the high RPM stops.
The blade is free to operate anywhere in the range between the mechanical stops, that the propeller governor makes it go. It may be operating right at the stops (such as the low pitch stops during low power settings) or the high pitch stops during high power settings. This is all part of the "alpha" range of operations, or the normal range.
In reverse, the pitch stops are removed, and the blade is allowed to be scheduled into a different pitch range. It's important to understand what reverse or beta is not, as much as it is to understand what constitutes the beta range. Beta is everything that alpha is not. One may think of feathered, or blade aligned with the wind, as the zero degree position...though this isn't technically accurate as the blade is twisted and the angle of incidence and AoA) varies along it's length. Everything in the range of operations when the propeller governor is controlling the propeller and it's working to impart energy to the slipstream behind the propeller, is the alpha range. At feather the blade is just trying to minimize drag and is aligned with the slipstream, and passing beyond that position as the propeller blade face is rotated to actually point slightly forward, is the beta range...the reverse range.
One way to think of it is hold your hand out the car window, flat, palm down, thumb side forward, as you travel down the road. Tilting your hand to a positive angle of attack, with wind catching the palm of your hand, produces lift, and it's doing something for you to hold up your hand. That's the alpha range. Tilting your hand so there's no lift up or down, no pressure on the back of your hand or on your palm, is the feathered position; very little drag. Tilting your thumb down so the pressure is on the back of your hand, that's a little like reverse...it's doing somewhat the opposite of what you did to produce positive lift. The example, however, ends there when comparing it to the propeller.
The propeller airflow is a little more complicated, of course, because merely by spinning it produces it's own airflow, and as the aircraft moves forward another element of complexity is added; the angle of the airflow meeting the propeller blade changes with the airspeed of the aircraft. Kind of makes your head spin, doesn't it?
From the cockpit, the alpha range is everything that the propeller governor is controlling when you want forward thrust. You move the power lever, that tells the engine what to do, and it in turn tells the propeller what to do based on the RPM that you've asked of the propeller. More power wanted, bigger blade angle, etc. The beta range, however, takes the propler governor's normal functions out of the equation. You're directly controlling engine power instead of letting the engine fuel control take charge, and you're directly scheduling the propeller blade angle using the throttles (or power levers or reverse levers...depending on the airplane). When moving into the beta range the propeller stops, the mechanical devices that limit the blade angle in normal operations, are removed. The blade is free to rotate past feather and into a condition that causes a great deal of drag...and absorbs a great deal of energy from the slipstream.
Reverse thrust and the beta range isn't so much pushing air forward as it is creating a lot of drag and absorbing energy. The amount of drag it creates depends on two things, speaking from the point of view of the cockpit. It depends on airspeed; the faster you're going when you move into the beta range, the more drag is created (because drag rise increases in proportion to the square of the airspeed; double the speed and get four times the drag). The beta/reverse drag is also a function of the engine power; the more reverse applied, the faster the engine tries to turn, and the greater the negative angle commanded by the pilot (it's just the way the propeller is mechanically rigged). The more energy imparted by the engine, the greater the drag, just as increasing the blade angle into the beta range increases drag...both occur at the same time.
To go into reverse, the power levers are retarded to idle, and in most cases, the propeller levers are lifted up and over a mechanical gate on the power quadrant in the cockpit. A small valve assembly in the propeller and governor (beta valve) either opens to allow controlling oil and fluid in the governor to bypass the governor, or in some cases closes to prevent the normal function of the governor. As the power levers (now called reverse levers...sometimes an extra set of levers riding "piggyback" on the pain power levers, sometimes the same set of levers used to control power in the alpha range) are moved aft and pulled "deeper" into reverse, the pilot is actually scheduling the blade angle manually. This is really what constitutes the beta range.
In the alpha range, the propeller governor schedules the blade angle based on what the pilot has requested. The pilot doesn't really control the propeller or the power; he just tells the engine what he wants by positioning the levers in the cockpit and watching the engine instruments, and the engine and propeller do the rest. In the beta range, however, the pilot schedules everything himself, and rudimentary limiting devices are put in place to make sure he doesn't give it too much blade angle, or too much power. In alpha, the propeller self governs, in beta, the pilot directly controls the prop and power.
As you can see, there are several ways to look at what constitues Beta and reverse. In the simplest sense, everything that isn't alpha range (or forward thrust) is beta. It's just not that simple. Many pilots think of normal range, beta, feather, and reverse as entirely different things...and think of beta as the region of prop control "that makes that funny sound" when taxiing. This is incorrect, but it's also a more common-use way of thinking of beta and reverse.
Another incorrect way of thinking about it is reverse thrust actually pushing air foward. This happens to some small degree (enough that some aircraft can be backed up slowly using reverse thrust), but it's not air being pushed forward that accounts for the effects of reverse thrust when landing. It's a massive increase in drag (a spinning propeller being driven by the slipstream experiences a greater drag rise than if you attached a big plywood disc out there, the same diameter as the propeller arc), and one in reverse experiences a dramatic drag rise above that. A better way to think about it is that because there's only so much drag to be had out of the slipstream and the propeller, the pilot makes more drag by altering the blade angle and then applying power.
What angles and ranges actually constitute "beta" differ slightly in definition (with respect to degrees, control positioning etc) by name between different manufacturers, but in general you can still think of everything that the propeller governor controls, which is producing positive thrust, as the alpha range, and everything else as the beta range. There are significant differences in the way different turboprop engines work, and the philosophy that drives them, and accordingly the way the propellers and their controls work, but if you think in terms of alpha/forward thrust, beta/everything else, you'll have the proper framework to address most any turboprop or piston engine with beta and reverse capability.