How does a chaff cloud create a false target for a radar and what determines its radar cross section?

A chaff cloud creates a false target for a radar by dispersing a large number of thin metallic dipoles (strips of aluminum-coated mylar or metallic wire) into the atmosphere, creating a cloud of radar-reflective material that produces a strong radar echo at the chaff cloud's location. The radar cross section (RCS) of the chaff cloud is determined by: the number of dipoles (N, typically millions per chaff bundle), the RCS of each individual dipole (sigma_dipole = 0.86 x lambda^2 / pi for a half-wave dipole at resonance, where lambda is the radar wavelength), and the total RCS of the cloud (sigma_cloud = N x sigma_dipole for randomly oriented dipoles at their resonant frequency; the dipoles are randomly oriented in 3D, and only approximately 1/3 are effectively reflecting at any given polarization, so sigma_cloud approximately N x 0.29 x lambda^2 / pi). For a chaff bundle with 10 million dipoles cut for X-band (lambda = 3 cm): sigma_dipole = 0.86 x 0.03^2 / pi = 0.000247 m^2 = -36 dBsm per dipole. sigma_cloud = 10^7 x 0.000247 / 3 = 823 m^2 = 29 dBsm (accounting for random orientation). This is comparable to a large aircraft or ship, creating a compelling false target. The chaff cloud effectiveness depends on: the radar frequency (the dipoles must be approximately lambda/2 long to resonate; different chaff cuts are used for different radar bands), the cloud density and volume (a tight cloud looks like a point target; a dispersed cloud occupies many range-Doppler cells and may be distinguishable from a real target), and the Doppler velocity of the chaff (chaff decelerates rapidly to wind speed, while a real target maintains its velocity; a Doppler-capable radar can often discriminate chaff from targets by their velocity difference).