Patent Number: 
Section: claims

1. A Fuel element comprising:a cladding tube having upper and lower sections and a middle section having a smaller diameter than the upper and lower sections;a gas plenum region in the upper section and an upper portion of the middle section;a metal fuel contained in the lower section;a fuel swelling absorption region in the lower section above the metal fuel; anda coolant disposed between sides of the metal fuel and the cladding tube in the lower section, in the fuel swelling absorption region, and in a lower portion of the middle section, whereina coolant density reactivity coefficient in the lower section has a negative value, anda coolant density reactivity coefficient in the upper portion of the middle section has a positive value. 2. The fuel element according to claim 1, wherein a length in a vertical direction of the upper portion of the middle section having the positive value of the coolant density reactivity coefficient is (100/Lf)2×Lf×40/100 where Lf is an effective fuel length of the metal fuel. 3. A fuel assembly comprising:a plurality of fuel elements;a wrapper tube surrounding the plurality of fuel elements;a coolant material passage formed between the plurality of fuel elements; each fuel element of the plurality of fuel elements including:a cladding tube having upper and lower sections and a middle section having a smaller diameter than the upper and lower sections, a gas plenum region in the upper section and an upper portion of the middle section, a metal fuel contained in the lower section, a fuel swelling absorption region in the lower section above the metal fuel, and a coolant disposed between sides of the metal fuel and the cladding tube in the lower section, in the fuel swelling absorption regions, and in a lower portion of the middle section, whereina coolant density reactivity coefficient in the lower section has a negative value, anda coolant density reactivity coefficient in the upper portion of the middle section has a positive value. 4. A core comprising: an inner core fuel region loaded with the fuel assembly according to claim 3; and an outer core fuel region loaded with the fuel assembly according to claim 3. 5. A core comprising: a plurality of fuel elements, each including a cladding tube having upper and lower sections and a middle section having a smaller diameter than the upper and lower sections, a gas plenum region in the upper section and an upper portion of the middle section, a metal fuel contained in the lower section, a fuel swelling absorption region in the lower section above the metal fuel, and a coolant disposed between sides of the metal fuel and the cladding tube in the lower section, in the fuel swelling absorption regions, and in a lower portion of the middle section; whereina coolant density reactivity coefficient in the lower section has a negative value, anda coolant density reactivity coefficient in the upper portion of the middle section has a positive value,the plurality of fuel elements is divided between an outer core fuel assembly and an inner core fuel assembly;the metal fuel is a ternary alloy of U—Pu—Zr, anda Pu content of the metal fuel in the fuel elements of the outer core fuel assembly is higher than a Pu content of the metal fuel in the fuel elements of the inner core fuel assembly. 6. The core according to claim 5, wherein an effective fuel length of the fuel elements in the inner core fuel assembly is shorter than an effective fuel length of the fuel elements in the outer core fuel assembly. 7. The core according to claim 5, wherein a length in a vertical direction of the middle section of the fuel elements in the outer core fuel assembly is shorter than a length in the vertical direction of the middle section of the fuel elements in the inner core fuel assembly.