A "flux tube" is a magnetically-confined conduit that allows charged particles to flow between one place in a planet's magnetosphere and another.
An "L-shell" is a subset of a planet's magnetic field lines that cross the planet's equator (for most planets, anyway) at the specified number of planetary radii from the planet's center.
In a uniform magnetic field, a charged particle traveling along field lines experiences no net force from the field. One traveling perpendicular to the field lines experience the Lorentz force, F = q (V X B), where q is the particle's charge, V is the velocity vector, and B is the field vector. Since that force is always perpendicular to the particle's velocity vector, this leaves the particle running around in circles! If the V vector is askew of the field vector, i.e. it has a component parallel to the magnetic field vector and a component perpendicular to the field vector, its velocity along the field lines remains unchanged, while the component perpendicular to the lines does its circular thing: the particle spirals along the field lines!
Net result: charged particles have an easy time of traveling along magnetic field lines, but traveling significant distances perpendicular to the field is nearly impossible. The flux tube is like a conductor surrounded by insulating material.
If there is a potential difference between the planet and a moon traveling in the magnetic field, charged particles can easily flow along the flux tube from the moon to the planet, or the other way. That flux tube will follow the usual toroidal geometry of a dynamo field, so for most moons the tube connects to the planet somewhere near the poles.
An L-shell is a toroidal surface within a dynamo field. If you imagine all the field lines that pass through the equatorial plane at a specified radius, say at 4 planetary radii from the center, and follow them all to the poles, you get a toroidal surface. Anything within that surface is said to be "at L = 4" or "at an L-shell of 4". L = 2 would intersect the equator at 2 planetary radii, and so on. So a flux tube within the L = 4 L-shell would be said to be "at L = 4".
The image below described further here, from Cassini shows (at ultraviolet wavelengths) two things: 1) the "normal" aurora at very high L-shells (thus closer to the pole), arising from charged-particle currents generated at many Saturn radii, where the solar wind and Saturn's magnetic field interact; and 2) the much smaller spot where the Enceladus flux tube, carrying the charged-particle currents, intersects Saturn's atmosphere and makes its own little aurora (in the white boxes).
As a Ph.D. student I was in a research group with people that worked with these all the time. Not only could the flux tubes guide charged particles, they can guide radio waves, so these folks would inject powerful radio signals into specific regions and see how the magnetosphere responded.
Enceladus 'Footprint' on Saturn
NASA's Cassini spacecraft has spotted a glowing patch of ultraviolet light near Saturn's north pole that marks the presence of an electrical circuit that connects Saturn with its moon Enceladus. This newly discovered patch occurs at the "footprint" of the magnetic connection between Saturn and Enceladus and indicates electrons and ions accelerating along magnetic field lines. White boxes indicate the location of this footprint, which scientists have long predicted but never before seen.
The patch glows because of the same phenomenon that makes Saturn's well-known north and south polar auroras glow: energetic electrons diving into the planet's atmosphere. However, the footprint is not connected to the rings of auroras around Saturn's poles.
The two images shown here were obtained by Cassini's ultraviolet imaging spectrograph on Aug. 26, 2008, separated by 80 minutes. The footprint moved according to changes in the position of Enceladus. In the image, the colors represent how bright the extreme ultraviolet emissions are. The lowest emission areas (one to two extreme ultraviolet counts per pixel) are in black/blue. The brightest emission areas (500 to 1,000 extreme ultraviolet counts per pixel) are in yellow/white.
The footprint appeared at about 65 degrees north latitude. It measured about 1,200 kilometers (750 miles) in the longitude direction and less than 400 kilometers (250 miles) in latitude, covering an area comparable to that of California or Sweden.
In the brightest image the footprint shone with an ultraviolet light intensity of about 1.6 kilorayleighs, far less than the Saturnian polar auroral rings. This is comparable to the faintest aurora visible at Earth without a telescope in the visible light spectrum.
The sun was illuminating Saturn's north pole from the left and the footprint is on the day side of the planet. The night side of the planet was to the right of the hashed line.
