Abstract I address the problem of estimating the time-rate-of-change of high-latitude Birkeland currents by using a string-of-pearls formation of satellites. Space series are calculated by linear interpolation of measurements made at the revisit times of the satellites. A lower bound on the total time derivative can be estimated as a function of distance along the orbit. Space series of the vertical component of electric current density, used as a proxy for field-aligned (Birkeland) current density at high latitude, are estimated from the along-track spatial derivative of Swarm magnetic field measurements residual to the CHAOS-7 internal field model. The results reveal non-negligible total time derivatives over periods shorter than 2 mins. Auroral Birkeland current densities derived from single-satellite traversals of magnetic field gradients can change dramatically in the time it takes a single satellite to cross a large-scale current system. In one example, during an overflight by the Swarm satellites of the THEMIS Fort Yukon all-sky imager on 1 December 2013, the vertical current density poleward of a visually quiescent auroral arc changes from

              $$\sim 0.3\ \mu \,\hbox {A}/\hbox {m}^{2}$$
              
                
                  ∼
                  0.3
                  
                  μ
                  
                  A
                  /
                  
                    m
                    2
                  
                
              
             upward to 
              
                
              
              $$\sim 1.0\ \mu \,\hbox {A}/\hbox {m}^{2}$$
              
                
                  ∼
                  1.0
                  
                  μ
                  
                  A
                  /
                  
                    m
                    2
                  
                
              
             downward in 13.7 s (corresponding to an along-track separation of Swarm A and B of 104 km). The variability of Auroral Birkeland currents, between 25 November 2013 and 31 December 2013, as estimated by the median of 
              
                
              
              $$|dj_z/dt|$$
              
                
                  
                    |
                    d
                  
                  
                    j
                    z
                  
                  
                    /
                    d
                    t
                    |
                  
                
              
            , reaches 
              
                
              
              $$15\ \hbox {nA}/\hbox {m}^{2}/\textrm{s}$$
              
                
                  15
                  
                  nA
                  /
                  
                    m
                    2
                  
                  /
                  s
                
              
             in the northern dayside auroral zone and exceeds 
              
                
              
              $$30\ \hbox {nA}/\hbox {m}^{2}/\textrm{s}$$
              
                
                  30
                  
                  nA
                  /
                  
                    m
                    2
                  
                  /
                  s
                
              
             in the pre-noon sector of the southern hemisphere.
          
          
            Graphic Abstract