Context : Stellar jets from young stars can be highly asymmetric and have multiple velocity components .

Aims : To clarify the origin of jet asymmetries and constrain the launch mechanism we study , as a test case , the physical and kinematical structure of the prototypical asymmetric flow emitted by DG Tau B .

Methods : The analysis of deep , high spectral resolution observations taken at the KECK telescope allows us to infer the properties and the spatial distribution of the velocity components in the two jet lobes .
From selected line ratios we derive the gas physical conditions ( the electron and total density , n _ { e } and n _ { H } , the ionisation fraction , x _ { e } , and the temperature , T _ { e } ) , as a function of both distance from the source and gas velocity .
The presence of dust grains in the jet is investigated by estimating the gas-phase abundance of calcium with respect to its solar value .

Results : The detected lines show broad velocity profiles at the base of the jet ( up to \sim 100 km s ^ { -1 } ) where up to three velocity components are detected .
At 5 ^ { \prime \prime } from the source , however , only the denser and more excited high velocity components survive and the lines are narrower ( \sim 10-30 km s ^ { -1 } ) .
The jet is strongly asymmetric both in velocity and in its physical structure .
The red lobe , which is slower ( \sim 140 km s ^ { -1 } ) and more collimated ( opening angle : \alpha \sim 3-4 ^ { \circ } ) , presents low ionisation fractions ( x _ { e } \sim 0.1-0.4 ) and temperatures ( T _ { e } < 5 10 ^ { 3 } K ) , while the total density is up to \sim 2.5 10 ^ { 4 } cm ^ { -3 } .
The blue lobe , faster ( \sim -320 km s ^ { -1 } ) and less collimated ( \alpha \sim 14 ^ { \circ } ) , is also less dense ( n _ { H } \sim 1 10 ^ { 4 } cm ^ { -3 } ) but highly excited ( T _ { e } up to \sim 5 10 ^ { 4 } K and x _ { e } up to 0.9 ) .
The estimated mass loss rate turns out to be similar in the two lobes ( \sim 6-8 10 ^ { -9 } M _ { \odot } yr ^ { -1 } ) , while the flux of linear momentum is 3 times higher in the blue one ( \sim 2.5 10 ^ { -7 } M _ { \odot } yr ^ { -1 } km s ^ { -1 } ) .
Calcium is strongly depleted with respect to its solar abundance , indicating that the jet contains dust grains .
The depletion is lower for higher velocities , consistent with dust destruction by shocks .

Conclusions : The similar mass loss rate in the two lobes suggests that the ejection power is comparable on the two sides of the system , as expected from a magneto-centrifugal ejection mechanism , and that the observed asymmetries are due to different mass load and propagation properties in an inhomogeneous environment .
The presence of dust grains implies that the jet is generated from a region of the disk extending beyond the dust sublimation radius .