1460889630-fa1a8aae-6d6c-44b1-a03f-14efe6f8a770

We claim:

1. A casing shoe for downhole use, comprising:
a body having at least one internal recess and a passage therethrough;
a cover mounted over said recess to protect said recess from debris accumulation resulting from cementing said body downhole;
said cover removable subsequent to cementing of said body to expose said recess.
2. The shoe of claim 1, wherein:
said cover is sealed to said body to define an enclosed annular space adjacent said recess.
3. The shoe of claim 2, wherein:
said annular space contains an incompressible material.
4. The shoe of claim 3, wherein:
said incompressible material is loosely packed.
5. The shoe of claim 4, wherein:
said cover is allowed to flex responsive to changing pressure conditions as said body is introduced downhole as a result of shifting of said incompressible material.
6. The shoe of claim 5, wherein:
said cover is removed by drilling through said shoe which allows said loosely packed incompressible material to be removed from adjacent said recess.
7. The shoe of claim 1, further comprising:
a tubular inserted through said shoe after removal of said cover for attachment to said recess.
8. The shoe of claim 7, wherein:
said tubular is attached to said recess by expansion.
9. The shoe of claim 8, wherein:
said body has a drift diameter outside of said recess and said tubular, after expansion into said recess, has a drift diameter at least as large as said drift diameter in said shoe outside of said recess.
10. The shoe of claim 8, further comprising:
a run in shoe at a lower end of said tubular that is released from said tubular by said expansion for retrieval through said body.
11. A well completion method, comprising:
running in a tubular having a shoe at its lower end;
providing a sleeve to cover a recess in said shoe;
cementing the tubular downhole;
removing the sleeve after said cementing to expose said recess.
12. The method of claim 11, comprising:
creating a sealed annular space around said recess with said sleeve.
13. The method of claim 12, comprising:
allowing said sleeve to flex in response to changing differential pressures across it as the show is lowered in the wellbore.
14. The method of claim 12, comprising:
providing an incompressible material in said annular space.
15. The method of claim 14, comprising:
loosely packing said incompressible material.
16. The method of claim 15, comprising:
drilling out said sleeve after said cementing; and
removing said incompressible material with the drill cuttings.
17. The method of claim 11, comprising:
inserting a tubular string after removal of said sleeve;
expanding said tubular string into said recess for support.
18. The method of claim 17, comprising:
providing a drift diameter for said tubular string after said expansion at least as large as the drift diameter of said shoe outside of said recess.
19. The method of claim 17, comprising:
connecting a run in shoe to the lower end of said tubular string for run in;
releasing said run in shoe from said tubular string by said expanding; and
retrieving said run in shoe to the surface.
20. The method of claim 19, comprising:
delivering said tubular string on a run in string further comprising a swage, a releasable anchor and a retrieving tool;
releasing said tubular string and said run in shoe from said run in string by driving said swage while it is selectively supported by said anchor;
capturing said run in shoe for return to the surface with said anchor and said swage as said run in string is removed.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1. A phased-array RF pulse generator, comprising:
at least one video-pulse generator configured to generate video pulses each having a leading edge;
an array of nonlinear and dispersive transmission lines, configured to generate RF pulses from the video pulses;
at least one sensor configured to detect the leading edges of the video pulses after they have passed along the transmission lines; and
a phase controller configured to set a velocity of the video pulses in each transmission line to put the detected leading edges, and hence the generated RF pulses, into a desired phase relationship.
2. A phased-array RF pulse generator as claimed in claim 1, in which the transmission line comprises:
a plurality of inductive elements and capacitative elements forming a LC ladder.
3. A phased-array RF pulse generator as claimed in claim 2, in which the inductive elements comprise: a saturable magnetic material, which causes the nonlinearity of the transmission line.
4. A phased-array RF pulse generator as claimed in claim 2 in which the capacitative elements comprise:
at least one nonlinear capacitor, which causes the nonlinearity of the transmission line.
5. A phased-array RF pulse generator as claimed in claim 1, in which the transmission line comprises: a plurality of further capacitative elements connected to the LC ladder to cause dispersion.
6. A phased-array RF pulse generator as claimed in claim 1, in which the transmission line is configured to provide nonlinearity and dispersion as a result of an impulse-excited gyromagnetic action.
7. A phased-array RF pulse generator as claimed in claim 1, in which each transmission line is associated with a velocity controller configured to control the velocity of the video pulses as they pass along the transmission line.
8. A phased-array RF pulse generator as claimed in claim 1, in which the at least one sensor that is configured to detect the leading edge is connected to a time-to-digital converter.
9. A phased-array RF pulse generator as claimed in claim 1, in which the generated RF pulses are microwave pulses.
10. A phased-array RF pulse generator as claimed in claim 1, in which the generated RF pulses have a duration of more than 3 RF cycles and less than 150 RF cycles.
11. A phased-array radar comprising:
a phased-array RF pulse generator according to claim 1.
12. A directed-energy weapon comprising:
a phased-array RF pulse generator according to claim 1.
13. A phased-array RF pulse generator, comprising:
at least one video-pulse generator configured to generate video pulses each having a leading edge;
an array of nonlinear and dispersive transmission lines, configured to generate RF pulses from the video pulses;
at least one sensor configured to detect the leading edges of the video pulses after they have passed along the transmission lines;
a phase controller configured to set a velocity of the video pulses in each transmission line to put the detected leading edges, and hence the generated RF pulses, into a desired phase relationship; and
a further sensor arranged to detect the leading edges of the video pulses at an earlier point in their propagation than the detection used in the setting of the phase of the RF pulses.
14. A phased-array RF pulse generator as claimed in claim 13, comprising:
a frequency controller configured to calculate time of flight of the video pulses from the detections of the leading edges by the at least one sensor and the further sensor and to adjust the velocities of the video pulses so that RF pulses of a desired RF frequency are generated in the transmission lines.
15. A phased-array RF pulse generator as claimed in claim 14, in which the frequency controller is configured to adjust velocities of the video pulses in accordance with transmission-line dispersion characteristics stored in a look-up table.
16. A method of generating RF pulses, comprising:
generating video pulses each having a leading edge;
using an array of nonlinear and dispersive transmission lines to generate RF pulses from the video pulses;
detecting the leading edges of the video pulses after they have passed along the transmission lines; and
controlling a velocity of the video pulses in each transmission line to put the detected leading edges, and hence the generated RF pulses, into a desired phase relationship.