SELECT, IN, LIMIT. How to make a request?

Question

MySQL

Good afternoon.
Table in the database

field_a	field_b
one	one
one	2
one	3
one	4
2	one
2	2
2	3
2	4
3	one
3	2
3	3
3	4

Request

SELECT * FROM `table` WHERE `field_a` IN (1, 2) ORDER BY `field_b` DESC

will return all rows where `field_a` is 1 or 2, sorted by `field_b`.
Question. How to make a query so that for each value of `field_a` 2 rows sorted by `field_b` are selected? That is, for the result to be

field_a	field_b
one	4
one	3
2	4
2	3

Answer 1

ORDER BY `field_a` ASC, `field_b` DESC

Answer 2

This option is correct, but rather slow.

SET @rank=0; 
SET @current_field=0; 
select a.field_a, a.field_b, 
@rank:=if(@current_field = a.field_a,@rank+1,0) as rank, 
@current_field:=a.field_a as current 
FROM  (select field_a, field_b from test2 where field_a IN (1,2)  
ORDER BY  field_a, field_b DESC ) as a having rank < 3;

Look, maybe it will be easier through GROUP_CONCAT(field_b ORDER BY field_b DESC) GROUP BY field_a and filter out the first N on the client side.