how we can make a pencil beam of microwaves generated from a microwave generator.
generator is not a magnetron but a microwave motion sensor.
please give me some technical information about it.
As IRstuff pointed out, and antenna would need to be 78 inches in diameter. But an antenna uses air with a dielectric constant of 1. If you use what is called a dielectric lense the size will be smaller. This substitutes a substance with a higher dielectric constant which makes the antenna smaller. I have seen specialized antennas using a dielectric antenna made of teflon
But, this is the extent of my knowledge in this area.
Nice CST simulation can be found in the link below. Midway down the web page is a active graphic showing the RF from a circular waveguide a few mm in diameter shaped into a planar wave using a dielectric lens only 74mm in diameter. The example is at around 25 Ghz. Exact numbers are not given, but probably around 2deg beanwidth.
A quick "crude" bench example can be done with a horn antenna and a plastic bottle of motor oil. Move the bottle back and forth a few inches outside the opening of the horn, and you can point where the beam is greatly narrowed. Maybe "crude" is a bad pun for a dielectric lens made from a bottle of oil, but I once saw it demonstrated very effectively. The difference in the velocity of propagation due the the dielectric focuses the wavefront into a more narrow beam.
Using an example of ultrasonics from nature, dolphins and some small whales use ultrasonic sound to "see" underwater. To get a narrow aperture, their bodies have a mass of fat in their heads with a different acoustic impedance to focus the ultrasonic sound. Basically a dielectric lens in the ultrasonic domain.
The only 'exception' (not really) to the relationship between antenna size and beamwidth are the Luneburg Lens antennas used for Satellite TV reception on aircraft. And even then, it's obviously not really an exception (except in purely practical terms of radome height, being very short compared to dish).
Not really applicable to the OP's question, but still quite interesting I think.
I believe I know these types of motion sensors at 10.525GHz. Not to 1 degree but it was never stated beam has to be 1 deg. Parabolic reflector will do wonders and even tin can properly positioned will give respectful directionality.