Relation Cross-Scans

Shielding Visible-Response Cross-Scan

A visible-response cross-scan varies how strongly the shielding cloud cancels the test charge, showing how the measured, screened charge shrinks versus the bare one row by row. The arithmetic is exact only for the stated responses, charges, and rows in the ideal Debye-shielding model. Real plasmas add collisions, sheath boundaries, nonuniform density, temperature spread, diagnostics calibration, and measurement/source uncertainty.

Visible charge is scanned across finite source and response ledgers. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Visible charge is signed source plus response

This is a finite signed shielding ledger. It does not claim a real exponential charge profile.

8 C+(−3 C)=5 C8\ \text{C}+(-3\ \text{C})=5\ \text{C}
Visible charge sourceSource, response, and visible labels are checked.sourcefieldresponse cloudsource=8 Cresponse=-3 Cvisible=5 Cscale2=12 m^2density=3lambda2=4 m^2

A stronger opposite response hides more source charge

The visible charge column is just signed addition. The zero row is complete finite cancellation, not field disappearance everywhere.

QsourceQresponseQvisible6−428−355−50\begin{array}{c|c|c}Q_{\text{source}}&Q_{\text{response}}&Q_{\text{visible}}\\6&-4&2\\8&-3&5\\5&-5&0\\\end{array}
Shielding response scanThe middle row is the checked source diagram.sourcefieldresponse cloudsource=8 Cresponse=-3 Cvisible=5 Cscale2=12 m^2density=3lambda2=4 m^2