Condign volumes 1 to 3

Read from the scan by GLM-OCR; expect the odd misread word.

# UNCLASSIFIED

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i. The objects are above the upper radar coverage capability (-100,000ft).

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S.26

## RADAR REFLECTIONS FROM PLASMA

5. A plasma is an assembly of small particles of three kinds, +ve, -ve and neutral; moving at random and colliding with each other. In all except very high current discharges there are many more neutral particles than charged particles. Electrons oscillate about a mean position, with angular frequency $ \omega_{0}=2\pi f_{0} $ , where $ \omega_{0}^{2}=4\pi N_{c}e^{2} / m $ The oscillations are linear and stationary and do not progress as waves. A plasma will reflect radar energy at all microwave frequencies below the "plasma frequency". A critical-density surface can be formed according to the density relationship:

$$
N _ {\mathrm {c}} = 1. 2 4 \times 1 0 ^ {1 0} f _ {\mathrm {o}} ^ {2} \left(\mathrm {c m} ^ {- 3}\right)
$$

f is in GHz. For example, a value of $ \geq1. 2 \times1 0^{1 2} \mathrm{c m}^{-3} $ will reflect X(I) Band and all frequencies below. Using these relationships the direct RF to density expression can be derived:

$$
f _ {0} = \sqrt {\frac {N _ {\mathrm {e}} . \mathrm {e} ^ {2}}{\pi \mathrm {m}}} \mathrm {o r} f _ {0} ^ {2} = \frac {N _ {\mathrm {e}} . \mathrm {e} ^ {2}}{\pi \mathrm {m}} + \frac {c ^ {2}}{\lambda^ {2}}
$$

$$
\text {w h e r e} \quad \mathrm {m} = \text {m a s s} 9. 1 1 \times 1 0 ^ {- 3 8} \mathrm {g}.
$$

$$
4. 8 \times 1 0 ^ {1 0}
$$

$$
(1. 6 \times 1 0 ^ {- 2 0}
$$

$$
1. 6 \times 1 0 ^ {- 1 9}
$$

This can be rearranged such that:

$$
\mathrm {f} _ {0} = 8 9 8 0 \sqrt {\mathrm {N} _ {\mathrm {c}}} \mathrm {H} _ {z}
$$

6. A plasma thickness may vary, hence:

- The location of the critical density 'mirror' is not necessarily at the outer extremity of the plasma.

- Some absorption of the incident energy can occur in the lower density region which the energy encounters before it penetrates to the depth of the critically dense region. This depends on the ambient air pressure.

- Incident radar energy may arrive at the plasma at various angles ( $ \theta $ ), hence:

$$
N _ {\mathrm {c}} = 1 2 4 \times 1 0 ^ {1 0} \mathrm {f} _ {0} ^ {2} \cos \theta . \mathrm {c m} ^ {- 3}
$$

- The refractive index of a plasma is always less than 1, given by:

$$
\mu = \sqrt {1 - \omega_ {\rho} ^ {2} / \omega^ {2}}
$$

where o is the radian frequency of the EM wave