The VX7044 is clearly a power device from the heatsink attached to a projection through the base, as shown below. The VX7044 is probably a klystron oscillator or similar velocity modulated device.
The paper label identifies this as an experimental valve with no guarantee of further supplies.
The top of the valve has a flange and this suggests that it would be clamped into a cavity or waveguide where the top square probe would couple power to the external circuit.
The heather and cathode assembly is at the side and can be seen at the top of this picture. In front of the cathode is a plate with a long thin rectangular hole to act as a kind of grid. The ribbon of electrons then passes through the main copper cylinder and on the other side is a grey metal electrode also on the outside of a slit in the main Copper tube.
The overall length is 141 mm.
The wide glass tube envelope is 29 mm in diameter and reduces to 18 mm diameter. Excluding the special base pins and heatsink is 79 mm tall.